am i responsible for vet bills for animal that was hurt on my property, that is not mine and was not on a leash?

Shallow fact patterns such as these, make it very difficult to respond directly. However, I will try my best for now, until you update your posting with a step-by-step account of the facts, coupled with details regarding the layout of your property, where the dog was from, how often dogs or others come onto your property, the extent of the injuries, who took the dog to the veterinarian, when you discovered the dog on your property, whether or not you have a fence, why your dog was outside, has your dog ever attacked anyone else, or any other animals, etc. Is it customary to allow dogs to roam freely in your community?

In legal terms, the dog is considered to be the property of the other. If you are responsible for the damage, then they can sue you for a civil claim called "Trespass to Chattel." Trespass to Chattel is "damaging one's property." However, to find you guilty under this claim, they would have to find that you intentionally caused the damage. This could be established by showing that you intentionally left your dog outside, with the intent of biting others (animals or people), if and when they trespass upon your property. If you did not intend the harm, then they do not have a claim under the Trespass to Chattel doctrine.

Another approach that they can take, is to sue you for negligence. However, legally, you are not responsible for "unknown trespassers" on your property. If you were not aware of the fact that the dog was on your property, then you are not responsible. An undiscovered trespasser will always lose in court, because they are a "surprise" to you.

But, if you were aware of the dog's presence, then he is considered a "known trespasser," and you are responsible for him. Discovered trespassers can win, as well as anticipated trespassers (both of which are “known trespassers”). Anticipated trespassers are those that you can anticipate coming onto your property, such as people that use your property as a shortcut, or where animals regularly come to drink from a creek, to mingle with your animals, etc. To win under this type of negligence claim, the other party must show that you were constructively aware of the danger, or had actual knowledge of the danger (your dog’s propensity to bite other dogs).

Can they sue you? Yes, of course - anyone can sue you for anything. Will they be successful? That depends.

If the facts are exactly as you state them, then I think they would have a hard time winning a suit against you for their vet bills. Did you call animal control or the police after the incident? If you did, that will help your case.

You should contact your homeowner's insurer for further guidance.