(a) No person shall maliciously, or willfully and without the consent of the owner, kill or injure a dog, cat, or any other domestic animal that is the property of another. This section does not apply to a licensed veterinarian acting in an official capacity.
(ORC § 959.02)
(b) Except as otherwise provided in this division, whoever violates division (a) of this section is guilty of a misdemeanor of the second degree. If the value of the animal killed or the injury done amounts to $300 or more, whoever violates division (a) of this section is guilty of a misdemeanor of the first degree.
(ORC § 959.99(B))
(c) This section does not apply to a person killing or injuring an animal or attempting to do so while endeavoring to prevent it from trespassing upon his or her enclosure, or while it is so trespassing, or while driving it away from his or her premises; provided within 15 days thereafter, payment is made for damages done to such animal by killing or injuring, less the actual amount of damage done by such animal while so trespassing, or a sufficient sum of money is deposited with the nearest judge of a county court or judge of a municipal court having jurisdiction within such time to cover the damages. The deposit shall remain in the custody of such judge until there is a determination of the damage resulting from such killing or injury and from the trespass. The judge and his or her bondsmen shall be responsible for the safekeeping of such money and for the payment thereof as for money collected upon a judgment.
(ORC § 959.04)