Ohio Rev. Code § 3521.03: Filling vacancy in United State House of Representatives.

When a vacancy in the office of representative to congress occurs, the governor, upon satisfactory information thereof, shall issue a writ of election directing that a special election be held to fill such vacancy in the territory entitled to fill it on a day specified in the writ. Such writ shall be directed to the board of elections within such territory which shall give notice of the time and places of holding such election as provided in section 3501.03 of the Revised Code. Such election shall be held and conducted and returns thereof made as in case of a regular state election. The state shall pay all costs of any special election held under this section.