Former NHL star Mike Comrie -- once married to Hilary Duff -- is under investigation by the LAPD for allegedly raping a woman at his L.A. home, but he claims it was consensual  ... TMZ has learned.

Law enforcement sources tell us the woman claims she met up with Comrie at a bar Saturday night and went back to his West L.A. condo. She claims he raped her multiple times.

The woman says she almost immediately went to Cedars-Sinai Medical Center nearby, and a rape kit was administered.  

Sources connected with Comrie say he's known the woman for a long time and acknowledges he had sex with her, but insists she gave full consent. The sources also say the encounter was a 3-way and the other woman has not filed any complaint.

We're told so far Comrie has not spoken to cops.