“Local governing entity” means:

  (a) In case of a single county health department, the county board of commissioners.

  (b) In case of a district health department, the county boards of commissioners of the counties comprising the district.

  (c) In case of a district health department which includes a single city health department, the county boards of commissioners of the counties comprising the district and the mayor and city council of the city.

  (d) In case of a single city health department, the mayor and city council of the city.

  (e) In the case of a local health department serving a county within which a single city health department has been created pursuant to section 2422, the county board of commissioners elected from the districts served by the county health department.