You shouldn't have to bring it into Ohio. I bought my car in NJ when I was there and registered it in Ohio. They have an out of state inspection policy. When I did it I had a police officer do the inspection. This might be the info, it has been a long time since I did it.
http://www.bmv.ohio.gov/registration_titling.stm#togOut-of-State Titles
When you are converting or transferring title to a vehicle that was last titled in another state, the following is required:
The actual Certificate of Title; copies are not acceptable. If your out of state title reflects an open lien, proper evidence of its extinction or a copy of the security agreement or loan contract covering the vehicle is required. If your title is held by a lienholder, any title office can provide the necessary paperwork to request the original title.
Out of State Inspection Form Any vehicle last previously registered or titled in another state must have a physical inspection, before being titled in Ohio. This is NOT a safety inspection. The inspection of your vehicle will verify the year, make, body type, model, and manufacturer's serial number or vehicle identification number (VIN). All license agencies offer this service as well as many car dealerships. Call ahead and ask for the service department.
You will be given the completed inspection form. Please contact the clerk of the Courts Title Office as well as where you get your inspection completed, for fees involved.