Brian is correct. listen to him. Your Cobra qualifys as a collector's vehicle.
Ohio Revised Code 3704.14
(3) The following motor vehicles are exempt from the inspection requirements of this section and applicable rules adopted under it:
(a) Vehicles over twenty-five years old, as determined by model year, on the date on which proof of an annual inspection otherwise would be required to be submitted with an application for registration of the vehicles under this section and Chapter 4503. of the Revised Code;
(b) Vehicles registered to military personnel assigned to military reservations outside this state, the district of registration of which is or is located in any county that is subject to this section;
(c) Passenger cars and noncommercial motor vehicles, as defined in section 4501.01 of the Revised Code, that weigh over ten thousand pounds gross vehicle weight;
(d) Commercial cars, as defined in section 4501.01 of the Revised Code, having a taxable gross vehicle weight of more than ten thousand pounds as provided in section 4503.042 [4503.04.2] of the Revised Code;
(e) Historical vehicles registered under section 4503.181 [4503.18.1] of the Revised Code;
(f) Licensed collector's vehicles as defined in section 4501.01 of the Revised Code;
§ 4501.01 Definitions.
(F) "Collector's vehicle" means any motor vehicle or agricultural tractor or traction engine that is of special interest, that has a fair market value of one hundred dollars or more, whether operable or not, and that is owned, operated, collected, preserved, restored, maintained, or used essentially as a collector's item, leisure pursuit, or investment, but not as the owner's principal means of transportation. "Licensed collector's vehicle" means a collector's vehicle, other than an agricultural tractor or traction engine, that displays current, valid license tags issued under section 4503.45 of the Revised Code, or a similar type of motor vehicle that displays current, valid license tags issued under substantially equivalent provisions in the laws of other states.