I'm pretty sure it's carry in the park..I may be wrong.Are you positive its against the law to carry in Ohio state parks?
I think its only the buildings, but it does become an issue if you fire it in a park.
State parks may be different from National parks, I guess I may need to do some more research.
https://traveltips.usatoday.com/ccw-rules-ohio-state-parks-108565.html