If you wish to register a trade mark or service mark in Ohio, you must fill out Form 555 and file it with the Secretary of State's Office. (Ohio Secretary of State) Form for registering a trademark or service mark in the state of Ohio.Get free patent and trademark legal assistance. Patent Pro Bono Program. How to File a Trademark in Ohio? We're going to talk about how to file your own trademark application with the united states patent and trademark office. Are you thinking of filing your trademark application yourself? To apply, prospective clients can fill out an application. Should Ohio inventors file a provisional application for a patent? Trademarks used in more than one state can be registered in the U.S. Patent and Trademark Office.