Ohio Revised Code Title XXXIX. Insurance § 3937.21

No insurance company issuing a policy of automobile or motor vehicle liability insurance shall be relieved of its contractual obligation to defend its insured against any claim on the basis of coverage for such claim being provided by any other policy, unless the insurer of such other policy has assumed and is performing the obligation to provide such defense. If the company pays to or on behalf of the insured any amount later determined to be due from another insurer it shall be subrogated to all rights of the insured against such insurer.

Any disputes between insurers regarding the obligation to defend shall be settled without expense to the insured by agreement between the insurers involved or, if they fail to agree, by arbitration or a declaratory judgment proceeding.