Hamm, 28, can be heard on an Upper Arlington police video telling an officer he'd had about eight drinks, WBNS-TV in Columbus reported. As Hamm sits handcuffed in the back of a cruiser, he asks officers to let him go and says, "I don't understand. I'm gonna kill you guys."
Hamm is charged with assault and two other misdemeanors. He was charged Saturday in suburban Columbus and is free on bond awaiting a Sept. 15 arraignment, according to online court records. His agent, Sheryl Shade, declined to comment Wednesday.
Hamm, whose hometown is Waukesha, Wis., is the 2004 Olympics all-around gymnastics champion, the only American with a men's world title and an Olympics all-around title.
He now works as an assistant coach at Ohio State. He and his twin brother, Morgan Hamm, also an Olympic gymnastics medalist, enrolled at Ohio State after the 2004 games and trained there until 2008.
Ohio State told the station that officials were aware of the arrest and would determine how to handle the matter after it is dealt with in court.
WBNS says a police report shows Hamm had fallen asleep as he was being driven home in the taxi.
The taxi driver, identified by the station as Abdinasir Elmi, told a reporter that Hamm had unintentionally locked the cab door and was trying to get out through the window. He said Hamm swore at him and elbowed him in the mouth as he tried to help him open the window.
Messages seeking additional details were left with Upper Arlington police spokeswomen.