Ohio Rev. Code § 2711.04
If, in the arbitration agreement, provision is made for a method of naming or appointing an arbitrator or an umpire, such method shall be followed. If no method is provided therein, or if a method is provided and any party thereto fails to avail himself of such method, or if for any other reason there is a lapse in the naming of an arbitrator or an umpire, or in filling a vacancy, then upon the application of either party to the controversy the court of common pleas in the county in which the arbitration is to be held shall, within fifteen days after such application is made, appoint an arbitrator or umpire, who shall act under said agreement with the same effect as if he had been specifically named therein. Unless otherwise provided in the agreement, the arbitration shall be by a single arbitrator.
R.C. §2711.04