From the Ohio fishing regulations:
It is unlawful for any person to possess a fish in any form or condition other than whole while on or when unloading the fish from a boat, while wading, or while fishing from shore on any waters in this state where a fishing license is required.

I did not know this! Also, I remember it saying something about it being unlawful to throw "offal" (fish guts) back into the water, but I didn't see it in my quick look.