The GBI identified the slain man as Rayshard Brooks, 27, of Atlanta.
Friday, officers responded to a call at 10:33 p.m. about a man sleeping in a parked vehicle in the drive-thru, causing other customers to drive around it, the GBI said in a statement.
Police gave Brooks a field sobriety test, which he failed, the GBI said. He resisted arrest and struggled with officers, the GBI said.
An officer drew his Taser and, witnesses said, the man grabbed it, the statement said. An officer then shot him.
Brooks was taken to a hospital, where he died, the statement said.
One officer was treated for an injury and released, the GBI said.
The GBI is investigating at the request of the APD, the statement said. Once completed, the case will be turned over to prosecutors for review.
CNN has reached out to the APD, GBI and the mayor’s office but they have not responded.
CNN’s Alex Meideros contributed to this report.