Prosecutors in the southern US city of Tulsa on Thursday charged a police officer who fatally shot an unarmed black man with first-degree manslaughter.

The shooting of Terence Crutcher on Friday, recorded by dashboard cameras and a police helicopter, lead to heightened tensions between yet another US police department and African-Americans.

In the video, the 40-year-old man is seen with his hands up, leaning against his car. He is then shot once by officer Betty Shelby and falls to the ground.

In a court filing, the Tulsa district attorney's chief investigator Doug Campbell said Crutcher was shot when reaching into his car's driver's side front window. Another responding officer used a Taser at the same time.

Campbell also said Crutcher had been mumbling to himself and that Shelby had made statements after the shooting that she had been "in fear of her life" during the confrontation.

"Officer Shelby reacted unreasonably by escalating the situation from a confrontation with Mr Crutcher, who was not responding to verbal commands and was walking away from her with his hands held up, becoming emotionally involved to the point that she overreacted," Campbell said.

Crutcher, who did not have a gun, died at a hospital from a single gunshot wound to the chest.

Shelby was charged with a felony count of first-degree manslaughter -- heat of passion, which carries a minimum sentence of four years in prison if convicted.

In the charging document, Tulsa County District Attorney Steve Kunzweller called her actions "unreasonable."

Responding to the charges during a news conference, the victim's twin sister Tiffany Crutcher applauded the quick action of the district attorney.

"We will stay vigilant as this process moves forward and join the others, peacefully, in demanding greater accountability and transparency from law enforcement," she said.

"We're demanding full prosecution. We want a conviction."

The Department of Justice has opened a federal civil rights probe, parallel to the investigation being carried out by local authorities.

Demonstrators in Tulsa, in the state of Oklahoma, had demanded that the officer be punished.

But protests have remained peaceful so far, unlike in Charlotte, North Carolina where the shooting death of a black man at the hands of police on Tuesday set off violent clashes between law enforcement and demonstrators.