Nelly's Rape Accuser Says She Will NOT Testify, Wants to Drop the Case (UPDATE)

4:20 PM PT -- Nelly's attorney Scott Rosenblum tells us ...the accuser's "reckless accusation, once investigated thoroughly, was exposed for what it was-a fabrication. A fabrication that has caused Nelly and his family to suffer emotionally and financially."

He's not satisfied though, and says he wants a public apology from the woman, and will recommend Nelly consider taking legal action against her.

The woman who accused Nelly of rape is refusing to testify, and wants the whole matter dropped ... TMZ has learned.

The woman's attorney, Karen Koehler, says her client has told the Auburn PD in Washington State, and the King County D.A. to "put a halt to the criminal investigation of [Nelly]. She will not testify further in a criminal proceeding against him."

Koehler says the young woman feels the system has failed her and she can't stand up to a celebrity. "Who will believe her. People are saying horrible things already. She cannot handle this. She is about to break."

Koehler added ... the woman was especially dismayed by the fact police told the media she had met with them and prosecutors -- after she was assured no one would know about the meeting until the investigation was closed.

TMZ broke the story ... the accuser told police Nelly raped her on his tour bus early last Saturday morning. He denied the allegation, and claimed she was motivated by greed, money and fame.