Police footage shows Terence Crutcher, who regularly attended church, walking away from officers with his hands up before being shocked with a stun gun and then fatally shot.
The video was released on Monday and a male voice from the police helicopter is audible, saying "time for a Taser" as Mr Crutcher, 40, walked to his car.
The voice then says: "That looks like a bad dude, too. Probably on something."
Mr Crutcher was shot in his car, unarmed.
It is not clear from the footage what led Betty Shelby, the officer who fired the fatal shot, to draw her gun or what orders officers might have given Mr Crutcher.
Mr Crutcher's twin sister, Tiffany Crutcher, has called for charges.
She says he was a dedicated Christian: "The big bad dude was my twin brother. That big bad dude was a father.
"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."
Local and federal investigations are underway to determine whether criminal charges are warranted over the shooting or if Mr Crutcher's civil rights were violated.
Ms Shelby has been placed on paid leave.
Speaking on Monday in Tulsa, civil rights lawyer Benjamin Crump said Mr Crutcher committed no crime and gave officers no reason to shoot him.
"When unarmed people of colour break down on the side of the road, we're not treated as citizens needing help. We're treated as, I guess, criminals - suspects that they fear," said Mr Crump.
He is representing Mr Crutcher's family, just as he did relatives of Trayvon Martin, an unarmed black Florida teenager who was fatally shot by a Neighbourhood Watch volunteer in 2012.
"So I guess it's a crime now to be a big black man," Mr Crump said. "My God, help us."
