Cops Called to Shia LaBeouf's Louisiana Home for Alleged Fight Between Exes

Cops were called out to Shia LaBeouf's New Orleans home a few times prior to his Mardi Gras arrest -- including once for an alleged fight between exes that allegedly included a punch below the belt ... according to police records obtained by TMZ.

Docs show a call for service at a NOLA home belonging to Shia for an alleged incident in early February between an unnamed man and the man's ex-girlfriend.

According to the police report, obtained by TMZ, cops say the man told police he was inside his home Feb 8. around 11:30 PM showing the place to his girlfriend when he heard a knock at the door and saw his ex-girlfriend entering the home and running toward them.

Police say the man told them he told his GF to run from his ex and he got between the women ... and that's when he claims his ex punched him in the groin area, making him "slump over and grimace due to the pain."

Cops say the man told them he dated the ex in November but broke the relationship off in December. Police also say the man told them he was not injured during the incident and refused medical services.

Police say the man was asked five risk questions about domestic violence ... and he told them he wasn't sure if his ex would seriously injure or kill him ... he told cops he knew "she was arrested for stabbing someone" in the past. The man also told police the ex threatens him in "every interaction" and that things were only "getting worse."

The report says an arrest warrant was issued for the ex-girlfriend.

As we first reported ... Shia was arrested last week in New Orleans after allegedly punching a bar employee, sparking a brawl before cops arrived. He was later charged with two counts of simple battery.

The arrest came months after Shia's split from estranged wife Mia Goth. We broke the story ... following the breakup, Shia relocated from Los Angeles to New Orleans in December, purchasing a 3-bedroom, 3.5-bath Uptown cottage for just over $1 million.

Shia hasn't been shy about going out in NOLA since the arrest ... and we got video of him packing on the PDA with a mystery brunette Saturday night at a bar just off Bourbon Street.