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Johnny Manziel's girlfriend told police the NFL star shoved her head into a window during a domestic dispute in their car on Monday ... and said both had been drinking ... this according to the police report.

Cops say Manziel was initially pulled on Interstate 90 at 6 PM after someone called cops to complain that Johnny's car had passed them on the shoulder at a high rate of speed.

During the stop, cops say Manziel's girlfriend, Colleen Crowley, said the couple had been arguing -- he pushed her head against the window -- and said she threw a wallet out of the window.

Cops said they noticed an abrasion on Crowley's arm -- but determined it was caused by Johnny restraining her when she tried to get out of the car while the car was on the road ... this according to the report obtained newsnet5.com.

Crowley reportedly said the two had been drinking in downtown Cleveland earlier in the day. Cops said they did not believe either Johnny or Colleen were intoxicated to the point where they should have been charged with a crime.

Colleen also told cops she did not want to press charges against Johnny. Ultimately, Johnny and Colleen left the scene together without being charged or cited for anything.

Manziel recently completed a stint in rehab back in April and said he was a changed man who was determined to regain everyone's trust and respect.

Crowley just issued a statement on Instagram saying, "J & I are good. I appreciate the people who stopped to check on us and call the police, I could see how it may have looked."