Cops to Nick Stahl -- You Look Suspicious ... EMPTY YOUR POCKETS

Does Nick Stahl look suspicious to you?? 'Cause cops in L.A. felt the "Terminator" star appeared so shady, they performed a full "empty your pockets" search on the guy in broad daylight.

Here's what we know ... Stahl was sitting on a street bench in West Hollywood on Monday when an L.A. County Sheriff's Dept. cruiser rolled up and the deputy called the actor over to the car.

During the interaction, the cop placed Stahl's hands behind his back, placed him against the squad car ... and began to pull items out of the actor's pockets.

But the cops didn't find squat -- and after a few minutes, the actor shook hands with the officer and went along with his day.

So, why did the cop feel compelled to search Stahl in the first place??

The L.A. County Sheriff's Dept. tells us ... Stahl was in a "high crime area" and appeared "suspicious" at the time. Cops wouldn't tell us WHY they felt Stahl appeared suspicious.

Cops say they also didn't force Stahl to empty his pockets -- the search was "consensual."

Stahl has had issues with the law in the past -- and back in December, he was cited for performing a "lewd act" in a Hollywood porn store.

We tried reaching out to Stahl for comment -- but we just couldn't get in touch with the guy.