Ohio Rev. Code § 4741.30
Upon the failure of any person to reclaim an animal left in the care of a licensed veterinarian or registered kennel owner, the veterinarian or kennel owner, at the end of a ten-day period starting with the day he gives notice as required under this section, shall be considered the legal owner of the animal and may send it to an animal shelter or pound. The veterinarian or kennel owner shall give written notice, either personally to the person who had left the animal, or sent by certified mail to his last known address. The notice shall specify the amount that shall be due for the care and treatment of the animal, the date on which the veterinarian or kennel owner will be considered to be the owner, and the location of the animal shelter or pound to which it will be sent for disposal. The person who had left the animal may redeem it prior to the expiration of the ten-day period by paying to the veterinarian or kennel owner the amount set forth in the notice for the care and treatment of the animal.
Upon receiving the animal, the animal shelter or pound shall keep, house, and feed it for a period of not less than three days. During this period, any person may purchase the animal by paying an amount equal to the sum of the expense incurred by the shelter or pound in maintaining the animal, the cost of any necessary registration tag, and the amount of money expended by the veterinarian or kennel owner in his care and treatment of the animal. Upon the redemption of the animal, the shelter or pound shall remit to the veterinarian or kennel owner the amount of money equal to that which he had expended in the care and treatment of the animal. If at the end of the three-day period no one has redeemed the animal, the shelter or pound may humanely destroy it.
R.C. §4741.30