We broke the story ... Faith Rodgers sued the singer last May, claiming he initiated "unwanted sexual contact" and had "abusive sex" with her in a Long Island hotel room after flying her to his concert in NY. She also reportedly filed a criminal report with Suffolk County PD in June.

But, according to an August 2018 supplemental police report -- obtained by TMZ -- Rodgers told cops that although they engaged in oral sex and sexual intercourse ... it was "without any verbal or physical resistance."

Cops say based on this -- along with the absence of any video or photo evidence of the incident from the hotel, law enforcement found the allegations to be "unprosecutable due to a lack of criminality."

R. Kelly's been off the hook for months, really ... we're told the case was never referred to the Suffolk County D.A.'s office for prosecution, so it had been closed last year.

As we reported, Rodgers secretly recorded R. Kelly in an attempt to get him to confess to sexually abusing her when she was 19 ... as well as plying her with drugs and alcohol and giving her an STD.

She also filed a criminal complaint in Dallas, but that case was recently closed for jurisdiction issues.