Ohio Rev. Code § 3505.36
When the board of elections of the most populous county of a district comprised of more than one county but less than all of the counties of the state has received from the board of every county in such district certified copies of parts of abstracts pertaining to an election in which only the electors of such district voted, such board shall canvass such parts of abstracts and determine and declare the results of the elections determined by the electors of such district. If more than the number of candidates to be elected to an office receive the largest number and an equal number of votes, such tie shall be resolved by lot by the chairman of such board in the presence of all of the members of such board. Such declaration of results by such board shall be in writing and shall be signed by at least a majority of the members of such board. It shall bear the date of the day upon which it was made, and a copy thereof shall be posted by the board in a conspicuous place in its office. The board shall keep such copy posted for a period of at least five days.
R.C. §3505.36