Probably. It might depend on when he was shot.
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Most, if not all, states have statutes addressing dangerous or nuisance dogs. A dog which left its own yard, entered a fenced yard and killed a domestic animal therein would almost certainly qualify for any action authorized under the statute - which is usually shooting the offending dog.
You can contact the OK and your county bar association for referrals if you really think you are the victim here.
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Most likely, but you do not give enough facts to answer the question.
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