What you are looking for is here:
OpenCarry.org - State Information For Ohio

Opencarry.org has info for all states in the the Union concerning open carry. They also do a good job listing the statutes so that you can read them for yourself if you so choose.

Do not let the naysayers get you down, there is nothing wrong with Open Carry. There is no "tactical disadvantage" and the police harass licensed people who carry concealed as well. As for "disorderly conduct" or "disturbing the peace" (which usually means that the police do not like you and cannot charge you with anything else) read your local statutes concerning them. There is very specific language for those types of crimes and openly carrying a firearm (when legal) is neither of those offenses.

I open carry sometimes, and conceal most of the time. I fully support open carry as there is no need to hide our firearms all of the time. Inside of the firearm enthusiast community there are many many people who are adamantly against open carry, just like there are people that do not care for "assault weapons" yet cherish their "deer rifles." This kind of splintering is foolish and unexamined. Carry openly if you wish, and be confident. (after spending time reading the law and knowing what you can and cannot do)

In closing, never surrender your fifth amendment right to keep your mouth shut when being questioned by the police. For a lecture on that topic, watch this video here:
YouTube - Don't Talk to Cops, Part 1

Remember, police can ask you anything they want and you do not have to answer any of it. If you refuse to answer their questions, you will be better off for it.