I found the below on the .PDF version of their form. It looks like OH requires a resident of the state or a corp that has a business address in the state.
Original Appointment of Statutory Agent
Pursuant to Ohio Revised Code §1705.54(A)(3), a foreign limited liability company must appoint a statutory agent to accept service of process on behalf of the company. We cannot accept articles of organization unless the statutory agent information is provided. The statutory agent must be one of the following: (1) A natural person who is a resident of this state; or (2) A domestic or foreign corporation, nonprofit corporation, limited liability company, partnership, limited partnership, limited liability partnership, limited partnership association, professional association, business trust, or unincorporated nonprofit association that has a business address in this state. If the agent is a business entity then the agent must meet the requirements of Title XVII of the Revised Code to transact business or exercise privileges in Ohio.
Northwest Registered Agent will serve as statutory agent for an annual fee. There are prob others companies out there as well. Good luck!