From the ODNR site:

It is unlawful...

To buy or sell any fish taken by sport fishing, including angling and trotlinefishing, taken from any water area in the state.

To transport and introduce any aquatic species (fish, invertebrate, plant) from one body of water to another.

For the public to tag and release fish into any public water area.

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

In addition:

Fillets must be kept whole until an angler reaches their permanent residence or until the fish are prepared for immediate consumption.

There is no requirement to keep any skin on fillets.

This does not apply to anglers with a receipt from a fish cleaning house or charter captain with states date, number, and type of fish possessed.

Fish may be transported whole or as a complete fillet while returning from the Lake Erie Islands on a commercial ferry boat.