The NYPD is investigating J.R. Smith for allegedly stealing a cell phone from a fan and throwing into a construction site ... TMZ Sports has learned.
Law enforcement sources tell us ... they got a call around 2:30 AM on Sunday morning from a guy who says he tried to take a picture with the Cleveland Cavs star outside of The Park, a hotspot in Chelsea.
Smith allegedly turned the fan down -- telling him no photos -- but he snapped one anyway ... and Smith snapped too.
We're told .