If a dog comes onto your property and attempts to attack you, you can shoot to kill.
Ohio Revised Codes, § 955.28 Dog may be killed for certain acts; owner liable for damages.
(A) Subject to divisions (A)(2) and (3) of section 955.261 [955.26.1] of the Revised Code, a dog that is chasing or approaching in a menacing fashion or apparent attitude of attack, that attempts to bite or otherwise endanger, or that kills or injures a person or a dog that chases, injures, or kills livestock, poultry, other 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 is not liable to prosecution under the penal laws which punish cruelty to animals.
(B) The owner, keeper, or harborer of a dog is liable in damages for any injury, death, or loss to 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.