Subject to Ohio R.C. 955.261(A)(2) and (3), a dog that is chasing or approaching in a menacing fashion or with an apparent attitude of attack, that attempts to bite or otherwise endanger a person, or that kills or injures a person, or a dog that chases, injures or kills livestock, poultry, another domestic animal, or other animal that is the property of another person, except a cat or another dog, can be killed at the time of that chasing, approaching, attempt, killing or injury. If, in attempting to kill such a dog, a person wounds it, he or she is not liable to prosecution under the criminal laws or ordinances which punish cruelty to animals.
The owner, keeper or harborer of a dog is liable in damages for any injury, death or loss to any person or property that is caused by the dog, unless the injury, death or loss was caused to the person or property of an individual who, at the time, was committing or attempting to commit a trespass or other criminal offense on the property of the owner, keeper or harborer, or was committing or attempting to commit a criminal offense against any person, or was teasing, tormenting or abusing the dog on the owner's, keeper's or harborer's property.
(ORC 955.28)