A US police department in Oklahoma has released video of an encounter in which an unarmed black man was shot dead by a white officer while his hands were up.

Video recorded by a police helicopter and a patrol car's dashboard camera were released by the Tulsa police department on Monday show 40-year-old Terence Crutcher being shocked with a stun gun and then shot dead.

In the encounter, which happened at about 7:40pm on Friday, Betty Shelby, a Tulsa police officer since 2011, shoots once and kills Crutcher while responding to a stalled vehicle report, according to the police department.

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A man in the helicopter above the scene can be heard saying during the incident: "Time for a Taser," and "That looks like a bad dude, too. Probably on something."

When a second police car arrived as back-up, Crutcher had his hands up as he walked away from Shelby, who was following him with her gun pointed at his back. She was soon joined by three more officers, according to the dashboard video of the second squad car.

Crutcher was shot less than 30 seconds after the second car arrived, US media reported.

Before the release of the incident's video and audio recordings, Police Chief Chuck Jordan announced that Crutcher had no weapon on him or in his four-wheel drive vehicle.

The initial moments of Crutcher's encounter with police are not shown in the footage.

Dashboard cam off

Shelby did not activate her patrol car's dashboard cam, said Tulsa police spokeswoman Jeanne MacKenzie. Only the second patrol car's dashboard cam was on.

Local and federal investigations are under way to determine whether criminal charges are warranted in the shooting or if Crutcher's civil rights were violated.

It is not clear from the footage what led Shelby to draw her gun or what orders officers might have given Crutcher.

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Initial police briefings indicated that Crutcher was not obeying officers' commands, but MacKenzie said on Monday that she did not know what Crutcher was doing that prompted police to shoot.

After the shooting, Crutcher could be seen lying on the side of the road, a pool of blood around his body, for nearly two minutes before anyone checked on him.

When asked why police did not provide immediate assistance once Crutcher was down, MacKenzie said, "I do not know that we have protocol on how to render aid to people."

Crutcher's twin sister, Tiffany Crutcher, called for charges on Monday.

"The big bad dude was my twin brother. That big bad dude was a father," she said.

"That big bad dude was a son. That big bad dude was enrolled at Tulsa Community College, just wanting to make us proud. That big bad dude loved God. That big bad dude was at church singing with all of his flaws, every week. That big bad dude, that's who he was."

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Source: Agencies