Yes, you do. Any recreational vessel has to be registered in Ohio. That includes USCG documented vessels used for recreational purposes.
According to the “Ohio Department of Natural Resources,” “registrations are required for every recreational boat in Ohio, including powerboats, sailboats, canoes, kayaks, pedal boats, and inflatable boats.” Link to the Ohio Department of Natural Resources.
To document your vessel, you can do so at our site here.