They have claws/nails so fingerprint identification of a trained dog is impossible or unthinkable. At least i've never heard of the police taking a dogs prints (if they even could)
So if you wanted to shoot someone and get away with it all you gotta do is hold the dog paw like a human hand and use that to manipulate the firing mechanism.
If the police test you for gunpowder residue make them also test the dog that way they can't determine who really pulled the trigger and the case gets thrown out