Being caught in possession of any gun that's not registered to you, or that you don't have a permit to carry, is ipso facto a felony in most jurisdictions. Getting caught with a gun anywhere near where a shooting crime occurred is even worse.

Most police departments use ballistics in shooting crimes. They try to retrieve spent bullets at the crime scene from victims' bodies, walls, furniture, etc. They then photomicrograph the bullets, which serves as a kind of fingerprinting process. Gun barrels are rifled--they have spiral grooves cut into the inside that impart a lateral spin to the bullets, stabilizing them in flight and making them more accurate (same principle a quarterback uses when he throws a spiral pass). The rifling imposes a pattern of grooves and marks on a bullet that can identify the maker of the gun (i.e., some use righthand rifling, others lefthand, and other markers).

The bullet's markings can, in many cases, be tied directly to the gun that fired it due to wear and/or imperfections in the gun barrel that show up on the bullet. If you just shot someone, and are caught at or near the scene with a gun, the police will fire your gun into a tank of water, retrieve the bullet, and match its markings against bullets retrieved from the victim's body. If they make a match, you're finished. PD's will send their results to the FBI, which has a database of ballistics of guns and bullets used in crimes. So, if you're caught with an unregistered weapon or are carrying without a permit--even if no crime can be attached to you--the PD will test-fire your weapon, retrieve the bullet, and send results to the FBI data base. If that data base matches the bullet from your gun to a bullet on file retrieved from a crime site, you could be charged with that crime. Then it'd be up to you to prove that you didn't commit that crime. That's why it's often risky to buy a used gun from someone else.