Greg Hardy's GF Claims He Pushed Her, Put Hands Around Her Neck Before Arrest

Greg Hardy's girlfriend claims the former NFL star pushed her onto a bed and held her down by her neck in an argument over cheating allegations prior to his arrest ... this according to documents obtained by TMZ Sports.

The woman called police around 2 PM on Wednesday to report a family violence in progress ... stating Hardy assaulted her and she had marks on her body. The woman also said Hardy fled their home in a white 2018 GMC Acadia after the physical altercation.

When cops arrived, the woman said the argument started when they were driving back from the park with their children -- Hardy asked his girlfriend what was wrong, and she replied they would address it when they were home ... as she didn't want to bicker in front of the kids.

Once they were home, the woman confronted Hardy about messages she saw on his phone ... and speculated he was unfaithful to her while he was out of town.

The woman claims Hardy told her to get out of his face, but she did not ... and he reacted by pushing her with both hands on her chest, forcing her on top of the bed.

The woman said Hardy then got on top of her and held her down with one of his hands around her neck ... but she was still able to breathe and did not lose consciousness.

She stated she started to kick Hardy ... leading him to grab her feet and push them away -- causing her whole body to turn.

Responding officers observed scratches and redness on the woman's arms ... and when asked to describe her pain on a scale of one to 10, she stated she felt a one.

After the incident, the woman claims Hardy got up and left the home ... only to be tracked down by police nearby.

Hardy confirmed an altercation took place ... but stated the woman poked him in the forehead with her index finger, which "hurt."

Hardy claimed he "moved her out of the way and placed her on the bed by grabbing her arms" -- but denied anything else happened.