Any local, exempted village, or city board of education, any educational service center governing board, or any combination of boards of such districts and centers, referred to in sections 3311.16, 3311.17, and 3311.18 of the Revised Code as the initiating unit, may make or contract for the making of a study pertaining to the need to establish within one county, or within an area comprised of two or more adjoining counties, a joint vocational school district, and for the preparation of a plan for the establishment and operation of a joint vocational school district covering the territory of two or more school districts within such county or counties. Any local, exempted village, or city school district in the county or counties may participate with the initiating unit in the cost of such study and plan. Such plan shall be submitted to the state board of education by the initiating unit.