That sort of thing isn't handled at the state level. Local laws apply to things like archery and air guns. If you live in Columbus proper there is no local law that forbids archery on your own land. You can't hunt but you can target shoot. Several of the satellite communities are OK with archery too.
If you lived in Gahanna as an example they have an issue if the projectile leaves your own land.
549.09 THROWING OR SHOOTING MISSILES.
(a) No person shall throw, shoot or propel an arrow, missile, pellet, stone, metal or other similar substance capable of causing physical harm to persons or property, in or on any public place, in or on the property of another, or from any private property into or onto any public place or the property of another. This section does not apply to supervised archery ranges or instruction nor when otherwise lawfully authorized.
(b) Whoever violates this section is guilty of a misdemeanor of the fourth degree.
Lawfully authorized would probably cover their urban archery program hunters. There is no complete prohibition but you need to keep the arrow on your own land.
What area do you live in exactly?