Ohio Rev. Code § 3709.10
When it is proposed that two or more general health districts unite in the formation of one general health district, the district advisory council of each general health district shall meet and vote on the question of union. An affirmative majority vote of the district advisory council shall be required for approval. When the district advisory councils have voted affirmatively on the question, they shall meet in joint session and shall elect a board of health for the combined districts. Each original general health district shall be entitled to at least one member on the board of health of the combined districts.
When such union is completed, the district shall constitute a general health district and shall be governed in the manner provided for general health districts. When two or more general health districts unite to form one district, the office of the board of health shall be located at the county seat of the county selected by the joint board of district advisory councils.
When two or more general health districts have been combined into a single district, the county auditor of the county selected by the joint board of district advisory councils as the location of the central office of the board of health shall be the auditor of such district and the county treasurer of such county shall be the custodian of the health funds of such district. When the budget of such combined general health district is a matter for consideration, the members of the budget commissions of the counties constituting the district shall sit as a joint board for considering and acting on such budget.
R.C. § 3709.10