Rodney King Dead -- Friends Are Not Buying Fiancee's Death Story

Two close friends of Rodney King think his fiancée isn't telling the truth about what happened leading up to his death ... and they've voiced their suspicions to cops, TMZ has learned.

As TMZ first reported, King's fiancee, Cynthia Kelley, says she was awakened by the sound of King banging on the window of their home just after 5:00 AM on Sunday ... and then heard him fall in the pool.

But sources close to King tell TMZ they heard Kelley tell the story several times to friends ... only the story changed a little bit each time and it seemed to them that she was lying about something.

We're told two of Kelley's friends who spoke with her in the hours following King's death have gone to police and spoke to a detective. Our source says the detective took down their story and their information and said he would be in touch.