how to check if a gun is stolen or been involved in crime?

With a rifle or shotgun, it pretty much can not be proven if it was used in a crime unless it was stolen from evidence, or was reported stolen.

With pistols sold in NYS before 4/1/12, they’d have to have collected shell casings from the scene of a crime and connect the dots through CoBIS, which no longer exists and never solved a single crime in NYS.