The following public officers, whether holding their elective office by election or appointment, and none other, are subject to recall:
(1) State officers: The governor, lieutenant-governor, secretary of state, state controller, state treasurer, attorney general, and superintendent of public instruction;
(2) Members of the state senate, and members of the state house of representatives.
(3) County officers: The members of the board of county commissioners, sheriff, treasurer, assessor, prosecuting attorney, clerk of the district court, and coroner.
(4) City officers: The mayor;
(5) Members of the city council.
(6) Special district elected officers for whom recall procedure is not otherwise provided by law.