(a) (1) The city or town council shall appoint a new commissioner to the board of commissioners of an improvement district created by the council if:

(A) There is a vacancy on the board because a commissioner has died or has ceased to reside in the state in which the improvement district was created; and

(B) Ten percent (10%) or more of the property owners of the improvement district petition the council calling attention to the vacancy on the board and requesting the appointment of a new commissioner to fill the vacancy.

(2) A commissioner appointed under subdivision (a)(1) of this section shall be a property owner in the improvement district in which the vacancy occurs.

(b) (1) A person shall cease to be a commissioner on the board of commissioners upon the filing of a petition with the city or town council that:

(A) Is signed by property owners representing ten percent (10%) or more of the assessed properties in the improvement district affected;

(B) Recites that the commissioner is no longer a property owner in the improvement district;

(C) Is accompanied by a corroborative certificate of an abstractor;

(D) Indicates a vacancy exists under § 14-88-303; and

(E) Designates a person to fill the vacancy who is a property owner of assessed property in the improvement district.

(2) The office is declared to be vacant from the date of filing the petition, and the council that created the improvement district shall name as commissioner of the improvement district to fill the vacancy the person named in the petition and recommended for commissioner of the improvement district if the person is a property owner in the improvement district.