Ky. Rev. Stat. § 67.310
In case either, or both, of the counties that have consolidated under the provisions of KRS 67.190 to 67.290 has a county health department, county library board, water district board, and other similar county agencies, the members thereof shall serve out the terms for which they were respectively elected. In case both counties have a board of the same type the consolidated county shall constitute a consolidated territory for the purpose of exercising all the functions of such boards, and such boards shall operate together as one (1) board until the expiration of the terms of all members. Provision shall be made for the election of a new board for the consolidated county as the expiration of the terms of the old members requires. In case only one (1) of the counties has a board of the type contemplated by this section the authority of such board shall be restricted to the confines of the territory that composed the original territory.
KRS 67.310