Drinkard said Deputy Director of Public Safety Keith Sanders made the decision early Tuesday to hand the case to the GBI.
"Basically, because questions have been raised about if should we be handling the case because of the people involved," Drinkard said. "This will give the public a level of comfort and assure them that it's beyond reproach."
Abdelmaseh told The Atlanta Journal-Constitution on Monday that her daughter, Hadassah, was playing on a swing when a man started haranguing her, telling her to get off because it was his granddaughter's turn.
The mother alleges that while Hadassah was lying on her belly in the swing, the man lifted it by its chains and shook it. She says he then lifted higher, with Hadassah still gripping the chains, and yanked the swing down hard, slamming the child to the ground.
Burger's report said Oakes told police his granddaughters had been waiting in line and the girl cut in. He said he only picked the girl up out of the swing, set her down and told her there was a line to wait in.
Neither Oakes nor his wife have returned calls from the AJC.
Under department policy, officers should write up incident reports when a complaint might warrant prosecution.
But Drinkard said one of the officers talked to Abdelmaseh's husband, and he told them not to file a report. Alfred Abdelmaseh, who wasn't at the park, said Monday he talked to an officer on his wife's cell phone, and the officer talked him out of it, telling him his wife was overreacting and "there's nothing here for us to even write up."
The girl wasn't hurt and had no signs of injury.