Johnny Manziel's GF: He Hit Me A Couple Times ... We Were Drinking

Johnny Manziel's girlfriend Colleen Crowley told police the Cleveland Browns QB hit her a "couple times" during their domestic dispute last week and admits they had been boozing earlier in the day ... this according to the police report.

As we previously reported, the Avon Police Dept. in Ohio responded to reports of a domestic dispute between Manziel and Crowley on Monday. When they arrived, Crowley had an abrasion on her left arm.

In the report, obtained by TMZ Sports, cops say Crowley told them Johnny had shoved her head against the glass of the car during an argument and then stated, "Mr. Manziel hit her a couple times in the car."

Crowley told cops she had 3 crown and cokes earlier in the day. Manziel, who recently completed a stint in rehab, told cops he had 2 drinks but sobered up before he got behind the wheel.

During the stop, Manziel's teammate Paul Kruger arrived to the scene -- but Crowley was angered by his presence and told him to leave ... "He doesn't need to be here."

Kruger told cops he was not a witness and only stopped because he happened to recognize Manziel's car as he was on the way to the Petitti Garden Center with his wife.

Cops took photos of Crowley's injury ... but say the "friction burn" on her wrist was the result of Manziel grabbing her wrist to keep her in the car.

In the report, cops say Crowley made it clear she did NOT want to press charges.

Cops determined Manziel was NOT drunk -- and eventually officers let the two leave together without making an arrest.