we had a similar situation here not long ago and a dog was shot while in a trap. The dog was found a while later, the dog owner and a few of the community were out to lynch the trapper but the county and city said their was nothing they could do, the trapper was legally in the right.
......around here, you shoot someone's dog, it better have it's teeth on your throat and not be stuck in your traps. There are huge fines and even prison sentences in the local paper every month about this kinda animal abuse. A good friend of mine works at the local vet's office and they treat dogs than have been shot as a crime and they and the local autorities go out of their way to find the person responsible. If that dog stuck in your trap has a collar and a tag on it, it is someone's pet and there are many ways to safely release that animal without getting bit. It ain't rocket science. If the dog is already dead, due to exposure or it being a conibear, you best call a warden or animal control to verify it. You also best hope the owner is happy enough to get their dog back, that they don't make you pay for the vet bills.