Can I sue for negligence if someone let my dog out of the house and he was hit by a car?

TECHNICALLY. . . YES. However, did you give permission for the "guest" to answer the door? Make a claim with your Homeowners Insurance . . . and see what happens (they'll probably deny it). You can try to sue the guest because he DID let the dog escape . . . but would a jury side in your favor or guests? Who is MORE credible? Also . . . guest is probably not collectable for the $13,000. Does Renters Insurance cover your property damages? Yes. Doggie is your property. You might have to sue your insurance company ("Bad Faith Insurance Claim") for TREBLE (triple) damages if they deny you coverage for doggie.

Who was the "somebody?" If it was a member of your family, then your homeowners insurance would not pay because it would be excluded by the contract. If the "somebody" was a child, you could sue but would be dependent on whether or not the kid was covered by homeowners insurance. If it was done on purpose, then no insurance would cover the intentional act. Now the next question is; "What is the value of the dog?" I believe that there may be some change in the law pertaining to the value of a family pet. The old law made animals to be "chattel," which is merely personal property, and therefore they were not worth much unless a show animal. I think that the law now gives them a more realistic value, but I am not really up on that part of the law.

I am sorry about the injury to your dog. Regarding your legal question, it may be possible to sue the individual will allow your dog to escape the property and therefore be injured. Your cause of action will most probably be against the individual who allowed your pet to escape. Generally it will not be a claim against your renter's insurance. There are a number of issues which you would like to discuss with an attorney prior to the time you make any irretrievable decisions.