The 'NYPD Blue' actress is being sued by a man named Dzhamal Badalov, who just filed legal docs -- obtained by TMZ -- alleging Kim rammed into his motorcycle while he was stopped at a red light back in Nov. 2022 ... this after he says she was driving erratically down Venice Boulevard in L.A.

Badalov claims witnesses saw Kim swerving in and out and lanes and driving erratically before she crashed into him -- which he alleges sent him flying into the road. He claims Kim tried driving away after the accident, but was initially stopped by bystanders.

Eventually, Badalov claims Kim got out of the car and called someone on her phone. He alleges she appeared completely out of and disoriented -- suggesting she was intoxicated. Badalov alleges that the person she was talking to on the other end attempted to pay him off to just let it go and not call the cops ... but Badalov says he refused to do so.

In the suit, he goes on to allege Kim was then instructed by the person on the phone to flee -- which he claims she then did. Now, he's suing her over the accident ... and wants damages.

Here's the other element to this ... we did some digging and found that a criminal case in L.A. has, in fact, been opened against Kim -- and she's been charged with hit and run. The claims made against Kim in a police report from that night -- obtained by TMZ -- essentially echo what's alleged in the lawsuit. She's due in court next week.