The 28-year-old's bizarre arrest in Columbus, Ohio was caught on police dash camera video. A cab driver says Hamm was drunk and refused to pay him a $23 fare.
Hamm can be heard on an Upper Arlington police video telling an officer he'd had about eight drinks. Police also say Hamm was combative.
As Hamm sat handcuffed in the back of a cruiser he asked officers to let him go and said, "I want you guys to let me go. Why won't you guys let me go? I don't understand. I'm going to kill you guys."
The cab driver says Hamm accidentally locked himself in the taxi and tried to go out the window. The driver says that's when Hamm elbowed him in the mouth.
Hamm is working as an assistant gymnastics coach at Ohio State as he trains for the London Olympics. There's no word yet how the arrest could affect his career.
"We have read about the unfortunate situation involving Paul Hamm in media reports, and we are certainly concerned for Paul," USA Gymnastics President Steve Penny said. "USA Gymnastics will wait for more information before commenting further."
Hamm was charged with assault and two other misdemeanors on Saturday. He is free on bond and is due in court for his arraignment Sept. 15.
Hamm is the only American man to win the Olympic (2004) or world (2003) all-around titles.
The Associated Press contributed to this story.