Trey Songz -- Walkz After Alleged Strip Club Money Attack

Trey Songz is officially off the hook in his strip club assault case ... after prosecutors decided they couldn't prove the rapper smacked a woman in the face WITH CASH during an album release party last August ... TMZ has learned.

We broke the story ... Songz was arrested for assault in NY after a woman at Club Perfection told cops Trey threw a "sum of United States currency" at her face, "causing substantial pain to her left eye."

It's unclear if the woman was a stripper ... or just one of those sexy waitresses that don't get naked (so disappointing, right?).

Officials investigated the incident ... and ultimately determined they couldn't prove he did anything illegal, so Trey is in the clear.

But the Queens D.A.'s office tells TMZ ... even if Trey did throw cash, "There would be no clear case of misconduct. There was just no high level of recklessness."