Ohio Revised Code Title XXXV. Elections § 3513.312

(B)(1) Except as otherwise provided in division (B)(2) of this section, the boards of elections of all the counties contained in whole or in part within the congressional district in which a vacancy occurs as described in division (A) of this section shall conduct the special election on a date designated by the secretary of state and 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 the case of a primary election, except that the secretary of state shall designate the deadline to file a declaration of candidacy or a declaration of intent to be a write-in candidate for the election.

(2) If only one person has filed a valid declaration of candidacy for the special election to be held under division (B)(1) of this section, or if no person has filed a valid declaration of candidacy, then no special election shall be held. If one person has filed a valid declaration of candidacy, the secretary of state, upon receiving certification of that fact from the board of elections of the most populous county of the congressional district, shall issue a certificate of nomination to the person and the person's name shall appear on the ballot as that party's candidate at the general election.