Quavo and Saweetie could soon be answering to the LAPD, because cops have opened an investigation into their elevator altercation … TMZ has learned.

Law enforcement sources tell us LAPD detectives have seen the video, obtained , showing the now ex-couple fighting over a video game console box, and cops want to meet with both parties, separately, to discuss what went down.

Our sources say the situation could be considered an instance of domestic violence, where both parties are in the wrong. Cops want to determine what happened before and after the elevator surveillance footage was captured.

the video — recorded last year — opens with a shot of Saweetie seemingly taking a swipe at Quavo. They continue to struggle over the orange gaming case, and then Quavo grabs Saweetie by the arm and drags her into the elevator, hitting the back wall and both collapse on the ground.

Quavo gets up, but Saweetie remains on the floor through the rest of their elevator ride. When it comes to a stop and she gets up and limps out. It doesn’t appear they exchanged any words while on the elevator.

As for the possible criminal case, we’re told once cops wrap their investigation, they’ll likely turn it over to the City Attorney to review for possible changes.