NBA player Royce White -- who famously missed his rookie season with the Houston Rockets due to mental health issues -- is at the center of a criminal investigation in Texas after allegedly beating up his then-girlfriend ... TMZ has learned.

We know ... White's ex-girlfriend Tania Mehra -- a Maxim model -- filed a police report on August 30 to report an incident that went down at Royce's Houston-area home back in June.

According to law enforcement records show someone called 911 on June 22 2013 to report a laceration above Tania's right eye. Cops say at the time Tania claimed she suffered the injury from an "accidental fall."

But Tania changed her tune last week ... and filed an incident report in which she claims she LIED on the night of the incident -- and says in reality Royce is to blame for her injury.