Ohio Rev. Code § 959.04
Sections 959.02 and 959.03 of the Revised Code do not extend to a person killing or injuring an animal or attempting to do so while endeavoring to prevent it from trespassing upon his enclosure, or while it is so trespassing, or while driving it away from his premises; provided within fifteen days thereafter, payment is made for damages done to such animal by such 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 such damages. Such deposit shall remain in the custody of such judge until there is a determination of the damages resulting from such killing or injury and from such trespass. Such judge and his bondsmen shall be responsible for the safekeeping of such money and for the payment thereof as for money collected upon a judgment.
R.C. § 959.04