Is there an Ohio state law that says financial institutions must do credit card cash advances for non-customers?

I am not sure about state, but you problably are contractually bound to with VISA/MC

^ Agree

You will want to check your agreement with Visa/MC/AMEX

I would be careful on this matter. In our area two banks have had a non-customer request a cash advance stating his mother had just passed away and he had flown in from California for her funeral. He needed to do a cash advance to pay for the funeral. He stated he did not contact his bank prior to leaving so the bank would have to call the bank using the number off the back of the card for the cash advance to go through. At that point a person will answer using the bank name off the front of the card. That person will then have the teller to press credit, and the force button, and they will then give you an authorization number that will allow the transaction to go through.
I have spoke to our card processor and they stated when you push the force button on the card machine it will take it offline and allow the charge to go through. The authorization really doesn’t even matter I was also advised this has been happening on the West Coast since 2011 and she called it the Funeral scam because that is normally the story that they use.