RICHMOND, Va. — Three Virginia police officers will not be charged with federal civil rights crimes for repeatedly using a stun gun on a black man who died soon after he was taken into custody, a prosecutor said Thursday.

Investigators found insufficient evidence to prove that the officers violated federal law by willfully using unreasonable force against Linwood Lambert Jr. in May 2013, U.S. Attorney John Fishwick Jr. said in a statement.

The announcement comes as people protest the treatment of blacks by police in Charlotte, North Carolina, and Tulsa, Oklahoma. Police in those cities are facing backlash after officers fatally shot black men.

Police car dash and hospital surveillance videos released last year show South Boston Police Officers Tiffany Bratton, Clifton Mann and Travis Clay using their stun guns repeatedly on Lambert after they took him into custody for a mental health evaluation on May 4, 2013. South Boston, a community of roughly 8,000, is in southern Virginia near the North Carolina border.

When they arrived at the hospital, Lambert kicked out the police cruiser’s window and ran toward the emergency room doors with his hands cuffed behind his back, the videos shows. As he ran away from the officers, they shocked him repeatedly, even after he fell to the ground.

Instead of taking the man to the hospital, the officers took Lambert to jail, telling him he was arrested for disorderly conduct and property damage. They shocked him again when he was put back in the cruiser, restrained in the back seat, the videos show. Lambert was later brought back to the same emergency room and pronounced dead about an hour after he was initially taken into custody.

Lambert told the officers that he used cocaine. The medical examiner’s office said his death was caused by “cocaine-induced excited delirium.”

The officers have said their use of force was appropriate because Lambert had become violent and was putting their safety at risk. Their attorneys also have rejected claims made by Lambert’s family that the man’s race was a factor, noting that one of the officers, Bratton, is also black, The South Boston News & Record reported.

Their attorneys didn’t immediately return email messages seeking comment on Thursday.

The FBI launched an investigation into Lambert’s death amid an outcry from the man’s family and civil rights leaders over the lack of answers about his death. Lambert’s sister, Gwendolyn Smalls, said Fishwick and Adam Lee, special agent in charge of Richmond’s FBI division, came to her house on Thursday to tell her the investigation was being closed.

Smalls said she’s deeply disappointed, but is grateful that her brother’s case received federal attention.

“My wish was to have the FBI do a thorough investigation and from what they told us today, I believe wholeheartedly that they did everything they could to see if my brother’s rights were violated,” Smalls said. “We will never heal. This will always be a pain in our hearts.”

To bring federal charges, prosecutors would have to show that the officers “willfully deprived an individual of a constitutional right,” the U.S. attorney’s office said. Investigators reviewed the videos, interview reports and the medical examiner’s report, among other things.

Investigators found there was no reliable evidence to suggest the officers shocked Lambert at the hospital door and in the patrol car for any reason other than to get him under control when he was acting erratically, the U.S. attorney’s office said.

“Mistake, misperception, negligence or poor judgment are not sufficient to establish a federal criminal civil rights violation,” Fishwick’s office said in the statement.

Halifax Commonwealth’s Attorney Tracy Quackenbush Martin announced in May that her office would not seek criminal charges against the officers.

The officers face a $25 million civil lawsuit filed by Smalls. A trial was originally set for early 2017, but the officers’ attorneys have asked for it to be pushed back until later in the year.

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Follow Alanna Durkin Richer on Twitter at twitter.com/aedurkinricher. Her work can be found at http://bigstory.ap.org/journalist/alanna-durkin-richer .