On their own motion or upon petition by twenty percent of the permanent political subdivision employees or the permanent noncertified employees of any school district, the political subdivision shall authorize and supervise a referendum of the permanent employees employed by that political subdivision on the question whether the employees elect to participate in the retirement system. If the majority of the employees vote in favor of participation in the retirement system, the political subdivision, notwithstanding anything to the contrary in chapter 40-46, may in its discretion enter into the agreement provided for in section 54-52-02.1. Notwithstanding provisions to the contrary in chapters 18-05, 18-11, and 40-45, the police department of any city, the fire department of any city, or both, may hold referendums among their employees on the question of whether their department should join the remaining city employees in participation in the retirement system established by this chapter. If a majority of the city police or city firefighters, or both, vote in favor of such participation, the governing body of the city must include the police and firefighters within any agreement entered into pursuant to section 54-52-02.1 and must arrange for discontinuance of any existing police or firefighters’ pension fund as provided by law.