License Information Ohio law requires every dog owner to renew the dog’s license between Dec. 1 and Jan. 31 of each year. To obtain or renew a dog license, contact the Cuyahoga County Auditor’s office by phone or online. Also, you can obtain them locally at the Discount Drug Mart at State and Wallings roads. The Cuyahoga County Auditor Office is located at 2079 East 9th Street Cleveland, OH 44115. You can reach their office at 216-443-7028.