Contact your shipper for requirements involving health certificates, etc...
But
The only thing that is different about Ohio, versus other states, is the native Ohio species... you must have a license with the Ohio Dept. Wildlife, to own a native species.
Now, use caution there, because what Ohio Wildlife wants to claim is native to Ohio, and what is REALLY native to Ohio may differ. For example, the Red Ear Slider is NOT a native Ohio species, but has been introduced and now lives here, and is therefore on the list... same as the Bullfrog and some other species.
And Ohio has a very small inclusion of Plains Gartersnakes (as one example) in a particular nature preserve, on the western border of the state. So, in their infinite wisdom, no one in Ohio can own a Plains garter, license or not, because its rarity allows them to call it "endangered", when the fact is, it just does not belong anywhere in the state, due to lack of habitat, except for that little sliver of habitat in the western part of the state.
Ohio DNR site (tool around in here and find the reptile/amphib regs...)