TMZ broke the story ... a woman filed a police report for rape back in December, claiming two sexual assaults in 1987 and 1990. Stallone believed the woman filed a false police report, and vigorously denied the allegation.

The L.A. County District Attorney's Office made the decision Tuesday not to charge Sly for the alleged attack ... citing insufficient evidence because none of the witnesses corroborated the woman's allegations. Sources connected with the case tell TMZ 2 witnesses contradicted the woman's story.

The statute of limitations had also expired.

Despite the statute of limitations having run out a long time ago, the Santa Monica Police Department still investigated. Stallone fired back at his accuser ... filing a police report claiming she committed the crime of lying on an official document.