The woman has told cops ... Cee Lo took her to a downtown L.A. restaurant in July. They had a drink and she says she remembers nothing after that. The woman claims the next thing she knew she was lying naked in a bed and Cee Lo was in the room.

We're told the woman, who does not live in California, almost immediately went to her local law enforcement agency and reported the incident. The matter was eventually referred to the LAPD.

Sources tell us ... LAPD detectives had the woman make a "pretext call" -- a call in which someone baits the other party into acknowledging a crime or other misdeed -- and it was recorded.

Sources involved in the case represent to TMZ ... Cee Lo is on tape, repeatedly apologizing and referencing MDMA (Ecstasy) -- though he does not specifically say he put it in her drink. Sources say Cee Lo told her he thought the drug would help them have an exciting time together. For the record, MDMA generally does not render people unconscious.

Sources connected with Cee Lo scoff at the claim, saying if the tape contained such admissions Cee Lo would already be under arrest.

As we first reported ... detectives went to the restaurant last week to determine if employees saw anything unusual between Cee Lo and the woman.

And we're told ... LAPD detectives will refer the matter to the L.A. County District Attorney's Office when the investigation is completed.

Sources connected to Cee Lo tell us ... the accuser went to a civil lawyer BEFORE going to police and demanded money from the singer to make the whole thing go away. Other sources tell us a different story -- that her lawyer called Cee Lo's manager to find out if the singer had any communicable diseases and never made any money demands.