Columbus Police responded to calls for a domestic dispute at Barrett's apartment. Barrett and the woman both declined to file charges, and police said that neither had visible injuries.
The case will be referred to the prosecutor's office, and any charges would have to be prompted by either Barrett or his ex-girlfriend.
Barrett, a redshirt freshman who started the entire regular season for the No. 4 Buckeyes before breaking his ankle against Michigan, accused the woman of refusing to leave his apartment, according to the police report.
In a separate call, the woman said Barrett choked her and flung her across the room.
Ohio State spokesman Jerry Emig told the Columbus Dispatch that the school was "aware of the report."
"We understand there were no charges filed," he told the paper. "We are looking into it."
The Ohio State staff, including coach Urban Meyer, is currently on the road recruiting.
According to the police report, Barrett said the woman ran at him and hit him before he pushed her away in self-defense, causing her to fall on a bed. The woman said Barrett confronted her in his bedroom and used his forearm to apply pressure on her neck and tried to take away her cell phone.
Barrett traveled with the Buckeyes last weekend to Indianapolis for the Big Ten championship game a week after suffering his broken ankle. He still has a cast on his foot and has had to use crutches and a modified scooter to get around as he begins his recovery after a record-setting season in which he led Ohio State with 45 total touchdowns.
The Associated Press contributed to this report.