Here's the part about helmets from the Ohio law. It specifies a top.
"(C)(3) Divisions (C)(1) and (2)(a) of this section do not apply to a person who operates or is a passenger in a cab-enclosed motorcycle
when the occupant compartment top is in place enclosing the occupants."
So if you had a removable top, and you took the top off, you'd have to have "safety glasses or other protective eye device". If under 18, on a learner's permit, or have had an endorsement for less than one year, a helmet is required.
For endorsements:
http://publicsafety.ohio.gov/links/bmv3741.pdf
"Cab-enclosed motorcycles do not require an endorsement."
Brings up an interesting point: If your vehicle has a removable top, then taking it off makes it not qualify as a cab-enclosed motorcycle. Which means the exemption for license endorsement doesn't apply? So you can drive a Slingshot with the top on without an endorsement, but if you take the top off you have to have an endorsement.... ?