I'm not sure if this is what you had in mind, but take a look at ORC ยง1129.12:
"No officer, director, employee, agent or attorney of any bank, except as provided by law, shall stipulate for or receive, or consent or agree to receive, any fee, commission, gift, or thing of value, from any person, firm or corporation, for procuring or endeavoring to procure for such person, firm or corporation, or for any other person, firm or corporation, any loan or extension or renewal of a loan or substitution of security from any bank, or the purchase or discount or acceptance of any paper, note, draft, check, or bill of exchange of any bank."
In English, I think this is saying that someone acting on behalf of the bank cant (in your case) charge a check cashing fee to a non-customer, but I dont read this section to proscribe the bank, itself, charging a fee. This is the closest I could find to your question.
If your bank is federally chartered, you might be able to ignore state restrictions like prohibitions against or limitations on the amount of such fees. Your federal regulator may have preemption determinations accessible at its website that will detail the extent of federal preemption of state and local check-cashing laws.