There is a couple of places here in Ohio that offer seasonal Police work.
Put N Bay on Lake Erie has a police department that hires seasonal officers for the summer months. They probably get pretty busy too, as Put N Bay is basically one big party island.
Cedar Point, also in the Lake Erie area, also hires seasonal officers. I worked there after I graduated college, and needed to get my police certification activated. It was a blast. They have both armed/certified officers, and non certified officers. The non certified officers do just about everything that the certified officers do, they just can't make arrests or carry a gun. Officers with Cedar Point are sworn in as special police with the city of Sandusky.
I also believe that Kings Island by Cincinnati also hire seasonal officers.
For any of the armed/certified positions, you would need an Ohio Peace Officer Certification. If you already have been through an academy in another state, most of your academy would probably transfer..but you would have to take a short refresher/law update to get your OPOTA certificate.
If you have any questions, just get a hold of me. I still have contacts at Cedar Point, and would be happy to help you out there.