Crawford, a 21-year-old African-American, was shot and killed by police inside a Dayton-area Walmart on Aug. 5 when officers responding to a 911 call about a man in the store with a weapon mistook the air rifle he was carrying for a real firearm.
Police claim Crawford was waving the pellet gun and refused orders to drop the toy.
Over 100 demonstrators protested Crawford's shooting in Columbus Monday.
Local news station WHIO reported that the Dayton chapter of the NAACP has launched its own investigation into Crawford's death and are waiting on Ohio Attorney General Mike DeWine to provide surveillance video and the results of the FBI's investigation before deciding on whether to launch a civil rights investigation.
Dewine said Tuesday a use-of-force expert was being called in to consult on the matter.
Dewine also announced a special grand jury will convene Sept. 3 to determine whether a crime was committed.