No, you wouldn't be able to run such a business without a license.
In Ohio, massage therapy is considered a subset of practicing medicine and requires a license through the State Medical Board. Massage therapy is broadly defined under state law and includes the "manipulation of soft tissue through the systematic external application of massage techniques." I have included a link to the relevant law below. That definition likely covers whatever services you were looking to provide.
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You may not practice massage without a license. Your jurisdiction is one of the states to require a license for the practice of massage. In your jurisdiction, the practice of massage is considered a limited branch of the practice medicine.