(a) The following authority shall order an election:
(1) the county judge, for the general election for officers of the county government;
(2) the mayor, for the general election for city officers in a city with a population of 1.9 million or more; and
(3) the governing body of a political subdivision, other than a county or a city described by Subdivision (2), that has elective offices, for the general election for those officers.
(b) If a law providing for an election relating to the affairs of a political subdivision does not designate the authority responsible for ordering the election, the governing body of the political subdivision shall order the election.