I strongly discourage asking anyone in the Law Enforcement community for advice. Look around this forum, and you will find numerous instances of LEO's giving incorrect information. Most of the time it is unintentional - they don't know the laws, and since you put them on the spot by asking, they guess. Contact an attorney for advice that you can rely on.
Click on OH from the main page of opencarry.org and you will find this summary:
Ohio is a traditional open carry state. However, they are also a home rule state with preemption for permit holders only. Additionally, a permit is required to have a loaded firearm in a vehicle and the firearm must be visible and on your person.
Be sure to verify this on your own, but since you have your CHL, you should be able to OC wherever CC is legal.
Edited to add: Welcome to OCDO!!