Central Park 'Karen' Case to Continue Despite Christian Cooper Not Cooperating

Amy Cooper -- AKA Central Park "Karen" -- isn't off the hook for making a false report against a man who asked her to leash her dog, despite the fact he doesn't want her prosecuted ... TMZ has learned.

As we reported ... the Manhattan D.A. announced this week his office initiated a prosecution against Cooper for Falsely Reporting an Incident in the Third Degree ... this, for the May 25 incident in which she called police claiming, "There's an African-American man threatening my life."

That man -- Christian Cooper (no relation), a birdwatcher -- made headlines shortly afterward when he said ... "She's already paid a steep price. That's not enough of a deterrent to others? Bringing her more misery just seems like piling on."

Amy was fired from her job and briefly lost custody of her dog after the video of her incident with Christian went viral.

So, Christian says if the Manhattan D.A. wants to pursue charges against Amy, that's his right ... but he will not be involved in the prosecution.

Well, TMZ's learned ... that's exactly what will happen. We're told the D.A.'s Office would like Christian to cooperate, but in this case, it's not necessary -- because he's technically not the victim ... it's the city. Besides, there's a smoking gun -- the video.

We reached out to the D.A.'s office ... it had no comment, other than to confirm Amy's scheduled to appear in court in October for her arraignment.