Officers at the Davie Police Dept. in Florida, according to docs obtained by TMZ Sports, say the incident all went down at around 11:44 PM on Monday night.

Cops in the docs say a woman claiming to be Young's ex-GF said the former baseball player showed up to her home and began banging on her door and ordering her to come outside.

The woman, cops say, then claimed when she stepped outside of her apartment, Young confronted her and got violent with her.

Cops say the woman told them Young punched her in the chest, and then shoved her to the ground as she attempted to flee and call 911.

In the docs, police say surveillance video captured the whole incident ... saying the footage revealed Young did hit the woman. Cops say the video also showed the woman "screeching in pain."

In the docs, cops note Young is 6 feet 2" and approximately 280 pounds ... while the woman is 5 feet 5", 130 pounds.

Cops claim in the docs Young ultimately fled the scene in a white SUV Maserati ... and say the 35-year-old blew through a stop sign and then hit 90 MPH in a 45 MPH zone.

Young was eventually arrested and booked on 4 charges ... including domestic violence. Jail records show he's still behind bars.

This is far from Young's first brush with the law -- the ex-Tampa Bay Rays outfielder has been arrested multiple times before, including in 2016 when he was accused of roughing up a hotel valet.