Law enforcement sources tell us 47-year-old Terry Bryant will not be prosecuted. As for why ... well, Bryant should send a big fat thank you to Frances.

We're told she was not willing to cooperate with investigators, so a judge dismissed the whole matter. Law enforcement sources tell us Frances wasn't down to work with cops from the beginning because she was embarrassed by the whole caper. She had merely left her Oscar to be engraved at the end of the ceremony, and then it turned into a whole media circus.

We're told Frances didn't even want to file a police report, but because the Academy of Motion Pictures actually owns the statuette ... it was listed as the victim, not Frances. However, she was the witness and prosecutors needed her testimony.

The D.A. tells us, "The District Attorney’s Office today told the court that we are unable to proceed at this time. The defense moved to dismiss the case, and Los Angeles County Superior Court Judge Sam Ohta dismissed it."

You'll recall ... Frances' golden statue went missing after the broadcast when she was backstage talking to the media. Bryant was seen parading around with an Oscar that was later identified as McDormand's ... and was eventually arrested.

McDormand won the statuette for her portrayal in 'Three Billboards,' and in her epic speech ... she called on more diversity in the industry, from top to bottom.