Sources in the know tell us she's been seeing a guy on the Beverly Hills PD for a few months. She's moved at lightening speed ... splitting with husband Stephen only months before she started dating the officer.

They met through mutual friends. She started dating him immediately and it took only a matter of weeks before he was staying at her home 5 - 6 nights a week. She's nuts about him.

This is a little eerie. Our sources say one of the reasons she likes him around so much is that he carries a gun, and she's scared of estranged hubby Stephen Belafonte. TMZ broke the story, Mel B has a restraining order against Belafonte, and one of her concerns is that she says he has a gun he's not allowed to possess because of a prior crime.

They're keeping the relationship "low key" ... both for his sake and hers. We're told his life is "complicated." But that hasn't stopped him, however, for showing up to tapings of "America's Got Talent" -- in plain clothes. He has also accompanied her to a number of social engagements.

Not everyone in Mel B's life thinks it's a swell idea she's dating the guy ... partly because of him and partly because she just got out of a bad relationship.

Still ... there's something symmetrical about Mel B going for a Beverly Hills Cop.