Coolio’s Baby Mama — He Brought Home a Chick and Beat Me

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should know better than to bring another woman home to the house he shares with his girlfriend … and he should also know better than to allegedly punch her in the face.

our sources has learned the rap legend — aka Artis Ivey Jr. — was popped on April Fools” Day after he allegedly pushed Anabella Chatman to the ground and punched her in the face.  And to add insult to injury … according to the police report, Coolio then hightailed it out of there with their toddler son and the other woman.

Actually … he didn”t get out clean.  Anabella says Coolio struck her with his car as he beat his hasty retreat — in fact, cops say she had tire marks on her leg.  Pretty compelling evidence.

Coolio tried convincing cops HE was the victim and that she scratched him in a jealous rage, but they weren”t buyin” what he was sellin” … so he was taken to the pokey.

 Calls to Coolio were not returned.