By Jack Healy, Julie Bosman, Alan Blinder and Julie Turkewitz, New York Times

KANSAS CITY, Mo. — Sha’Quille Kornegay, 2 years old, was buried in a pink coffin, her favorite doll by her side and a tiara strategically placed to hide the self-inflicted gunshot wound to her forehead.

She had been napping in bed with her father, Courtenay Block, late last month when she discovered the 9-millimeter handgun he often kept under his pillow in his Kansas City, Mo., home. It was equipped with a laser sight that lit up like the red lights on her cousins’ sneakers. Mr. Block told the police he woke to see Sha’Quille by his bed, bleeding and crying, the gun at her feet. A bullet had pierced her skull.

In a country with more than 30,000 annual gun deaths, the smallest fingers on the trigger belong to children like Sha’Quille.

During a single week in April, four toddlers — Holston, Kiyan, Za’veon and Sha’Quille — shot and killed themselves, and a mother driving through Milwaukee was killed after her 2-year-old apparently picked up a gun that had slid out from under the driver’s seat. It was a brutal stretch, even by the standards of researchers who track these shootings.

These are shooters who need help tying their shoelaces, too young sometimes to even say the word “gun,” killed by their own curiosity.

They accidentally fire a parent’s pistol while playing cops and robbers, while riding in a shopping cart, after finding it in the pocket of the coat their father forgot to wear to work. The gun that killed Sha’Quille last Thursday was pointing up, as if being inspected, when it fired.

They are the most maddening gun deaths in America. Last year, at least 30 people were killed in accidental shootings in which the shooter was 5 or younger, according to Everytown For Gun Safety, a gun control advocacy group that tracks these shootings, largely through news reports.

With shootings by preschoolers happening at a pace of about two per week, some of the victims were the youngsters’ parents or siblings, but in many cases the children ended up taking their own lives.

“You can’t call this a tragic accident,” said Jean Peters Baker, the prosecutor of Jackson County, Mo., who is overseeing the criminal case in Sha’Quille’s death. Her office charged Mr. Block, 24, with second-degree murder and child endangerment. “These are really preventable, and we’re not willing to prevent them.”

Gun control advocates say these deaths illustrate lethal gaps in gun safety laws. Some states require locked storage of guns or trigger locks to be sold with handguns. Others leave safety decisions largely to gun owners.

Twenty-seven states have laws that hold adults responsible for letting children have unsupervised access to guns, according to the Law Center to Prevent Gun Violence, though experts say such measures have, at best, a small effect on reducing gun deaths. Massachusetts is the only state that requires gun owners to store their guns in a locked place, though it has not stopped youngsters there from accidentally killing themselves or other children.

Gun rights groups have long opposed these kinds of laws. They argue that trigger locks can fail, that mandatory storage can put a gun out of reach in an emergency, and that such measures infringe on Second Amendment rights.

“It’s clearly a tragedy, but it’s not something that’s widespread,” said Larry Pratt, a spokesman and former executive director of Gun Owners of America. “To base public policy on occasional mishaps would be a grave mistake.”

In Kansas City, Sha’Quille’s family is trying to come to grips with her death and the murder charge facing Mr. Block. In interviews, several relatives said they did not believe he deserved to be convicted of felony murder, but some questioned his judgment in leaving a loaded gun out while he slept as well as his actions after he discovered that his daughter was grievously wounded.

According to court records, Mr. Block told the police that immediately after the shooting, he went to the bathroom, wrapped the gun in a shirt and put it into a vent in the floor. He then ran outside carrying his dying daughter and yelled for a neighbor to call for help. He was also charged with evidence tampering.

Sha’Quille’s mother, Montorre Kornegay, said that she had recently separated from Mr. Block after more than five years together, but that they remained close. She said he loved the girl, whose first word was “Daddy.” When he called Ms. Kornegay from jail, he told her he was sorry and talked about how much he missed Sha’Quille.

The girl was just 2, but wanted to be older, telling people she was already 5. She would run through the house, playing her own private game of peekaboo, relatives said. In a cacophony of squeaky children at home, relatives could always distinguish Sha’Quille’s low, raspier voice. One day, she’ll be a singer, they told one another.

“What happened was wrong,” Ms. Kornegay said. She said that she did not think Mr. Block deserved to face a murder charge, but that he had behaved irresponsibly. “Why didn’t you stay up and watch her?”

Parents, police officers and neighbors from Georgia to California are asking similar painful questions this week. Here are some of their stories.

‘Stay With Me’

In 2015, there were at least 278 unintentional shootings at the hands of young children and teenagers, according to Everytown’s database. During the week in April when Sha’Quille and the other children died, there were at least five other accidental shootings by children and teenagers. Alysee Defee, 13, was shot in the armpit with a 20-gauge shotgun she had used for turkey hunting in Floyd County, Ind. Zai Deshields, 4, pulled a handgun out of a backpack at her grandmother’s home in Arlington, Tex., and shot her uncle in the leg.

A child who accidentally pulls the trigger is most likely to be 3 years old, the statistics show.

Holston Cole was 3, a boy crackling with energy who would wake before dawn, his pastor said. He loved singing “Jesus Loves Me” and bouncing inside the inflatable castle in his family’s front yard in Dallas, Ga.

About 7 a.m. on April 26, he found a .380-caliber semiautomatic pistol in his father’s backpack, according to investigators. The gun fired, and Holston’s panicked father, David, called 911. Even before a dispatcher could speak, Mr. Cole wailed “No, no!” into the phone, according to a redacted recording.

Mr. Cole pleaded for his 3-year-old son to hold on until the ambulance could arrive: “Stay with me, Holston,” he can be heard saying on a 911 tape, his voice full of desperation. “Can you hear me? Daddy loves you. Holston. Holston, please. Please.”

Holston was pronounced dead that morning.

The local authorities have been weighing what can be a difficult decision for prosecutors and the police after these shootings: Whether to charge a stricken parent or family member with a crime. While laws vary among states, experts said decisions about prosecution hinge on the specific details and circumstances of each shooting. What may be criminal neglect in one child’s death may be legally seen as a tragic mistake in another.

Officials with the Paulding County Sheriff’s Office have suggested that they expect Mr. Cole to face, at most, a charge of reckless conduct.

“Anything that we do, criminally speaking, is not going to hold a candle to the pain that this family feels,” said Sgt. Ashley Henson, a spokesman for the sheriff’s office. Sergeant Henson said investigators had sensed early on that the shooting was accidental. “You want to be able to protect your family and take care of your family, but on the same hand, you’ve got to be safe with your weapons,” he said.

Some gun control groups have urged states and district attorneys to prosecute such cases more aggressively, saying that, grief aside, people need to be held responsible for what are easily preventable deaths.

Brent Moxey, the pastor who officiated at Holston’s funeral, said the boy’s father was already haunted. “I think he runs the scenario over and over and over in his mind.” Mr. Moxey said the family — which did not respond to a message left at their home seeking comment — was still asking for privacy.

About 1,000 mourners attended Holston’s funeral on April 30, remembering a boy who loved superheroes and would sometimes wrestle cardboard boxes. The day he died, he spent time alongside his mother, Haley, as she read the Bible, playing with the highlighter pen she used to note passages, Mr. Moxey said.

“This little boy loved to tinker and to play, and he loved to get into things,” Mr. Moxey said, describing the very impulse that probably led to Holston’s death. “He loved to figure out how stuff works.”

A Ringing Purse

In Indianapolis, Kanisha Shelton would stay protectively near her 2-year-old son, Kiyan, watchful of the stray dogs known to roam through the neighborhood.

But on the night of April 20, Ms. Shelton stepped away from the boy, leaving him in the kitchen while she was upstairs. She had placed her purse out of his reach on the kitchen counter, but when her phone started ringing, the boy apparently pushed a chair close to the counter, climbed onto it and reached for the purse, according to an account from a cousin, John Pearson. There was also a .380-caliber Bersa pistol in it.

Just after 9 p.m., Ms. Shelton heard a loud bang and rushed downstairs. There, in the kitchen, she found Kiyan lying on the floor, bleeding from a gunshot wound to the chest. He was rushed to a local children’s hospital, where he was pronounced dead.

Ms. Shelton’s mother, who answered her daughter’s cellphone, said the family did not want to speak about the death. No criminal charges have been filed.

The police in Indianapolis said such scenes were becoming more common. “The mother was obviously very shaken up,” Capt. Richard Riddle said. Indeed, on Sunday night, another child, 10 years old, died in what the police say appears to have been another accidental shooting.

A 2013 investigation by The New York Times of children killed with firearms found that accidental shootings like these were being vastly undercounted by official tabulations, and were occurring about twice as often as records said.

Dr. Garen J. Wintemute, an emergency physician and a researcher at the University of California, Davis, who studies the public health effects of gun violence, said that nearly everyone — from toddlers to adults — can fail to accurately distinguish toy guns from real guns, loaded guns from unloaded ones.

“That doesn’t stop them from playing with it,” he said.

Mr. Pearson said he sympathized with Ms. Shelton and thought of Kiyan’s death as a tragic accident. “It was up on the counter, so I do think she thought she put the gun away, out of the baby’s reach,” Mr. Pearson said. “She’s going to be in a living hell.”

Essie Jones, who lives across the street, said Ms. Shelton had recently taught Kiyan to ride a small bicycle with training wheels, guiding him on the bike in the driveway. “They’d be up in the yard playing,” she said. “He was very happy.”

In a condolence book online, Dianna Mitchell-Wright, who identified herself as “Auntie,” wrote of her anguish over losing the boy she had nicknamed “My Main Man.”

“All I have are memories,” she said, “and your pictures in my cellphone.”

Anguished Goodbyes

The coffin that held Za’veon was no bigger than a piece of carry-on luggage, and it was so light that two pallbearers easily carried it through the packed St. Paul Missionary Baptist Church in Bermuda, La.

His full name was Za’veon Amari Williams, but to his family in Natchitoches, the 3-year-old was known as Baby Zee. On April 22, he found a pistol and shot himself in the head, according to Detective John Greely of the Natchitoches Police Department. When paramedics arrived, they found the mother cradling the boy and crying that he was not breathing, according to KSLA News 12.

The police arrested a companion of the mother, Alverious Demars, 22, on charges of negligent homicide and obstruction of justice. Detective Greely said that the police believed that the pistol belonged to Mr. Demars, and that he hid it after the toddler shot himself. The police have not found the weapon.

“As a responsible adult it’s his obligation to secure that — to make sure a child does not get ahold of it,” Detective Greely said, explaining why Mr. Demars had been arrested.

The family declined to speak, but in a Facebook post, the boy’s mother, Destiny Williams, wrote that she had not been able to sleep and was a “useless sad waste.” “I can’t take life,” she wrote. “Why is it so cruel and unrelenting and unforgiving.”

The funerals for these children were filled with a similar anguish.

At the funeral for Baby Zee, the wails and screams grew so loud during a final moment of goodbye that ushers closed the church doors to give the family privacy. In Georgia, Holston’s father tearfully read a letter that reflected on how the family used to sing “Jesus Loves Me.” At the Kansas City funeral for Sha’Quille, family members crumpled as they looked into the coffin, shaking with tears or kissing her.

The day after Sha’Quille was buried, her maternal grandmother, Pamala Kornegay, reflected on the girl who was missing from the cluster of grandchildren who sat coloring on her living room floor. Ms. Kornegay said she was not angry with Sha’Quille’s father.

“We’re just upset,” she said. “It was careless. It could have been prevented.” So senseless, she said, because Mr. Block had loved his daughter so dearly.

“He would take a bullet for her,” she said.

Mitch Smith contributed reporting from Chicago; Ian Lovett from Wilseyville, Calif.; Jack Begg from New York; and Nathan Magner from Bermuda, La.

To Learn More:

            Beware of Online Advice on Safely Storing Guns at Home (by Steve Straehley, AllGov)

Toddlers have Shot Themselves or Someone Else At Least 43 Times This year (by Steve Straehley, AllGov)

University Researchers Protest Defunding of Gun Safety Research (by Matt Bewig, AllGov)