6:50 PM PT -- Gordon's girlfriend told police he was pissed off because he thought she was trying to hook up with one of his friends at a sports bar Friday night. She says they got home from the bar and argued into the early morning.

When she tried to leave, Gordon started "punching and hitting her and refused to let her leave." She says he also snatched a laptop she was trying to use to communicate with her sister.

According to the police report, she was only able to leave when she woke up Gordon's mother, who apparently also lives in the home. Gordon's mother drove to the gf's home ... where the gf's sister then took her to the hospital.

Nick told police he did not hit the woman, and claims she attacked him ... and wanted to press charges against her.

Nick Gordon -- Bobbi Kristina Brown's boyfriend who was found legally responsible for her death -- has been arrested for domestic violence and kidnapping his current girlfriend.

Gordon was taken into custody Saturday afternoon in Sanford, Florida. He's facing 2 charges -- domestic violence battery and kidnapping/false imprisonment of an adult.

Sources close to the girlfriend tell TMZ ... Nick allegedly beat her up Friday night so badly she had to go to the hospital.

Law enforcement tells us ... the girlfriend filed a report at the police station Saturday morning claiming she'd been battered and not allowed to leave their residence. We're told officers went to the residence and found Nick at the pool area.

We've obtained photos of the girlfriend's alleged injuries.

You may recall ... Gordon's on the hook for $36 million to Bobbi Kristina's estate, and he's still under criminal investigation for her death.