(a) On the Tuesday following the first Monday in November, 1972, and every four (4) years thereafter, the qualified voters of cities of the second class shall elect a recorder, a treasurer, or a recorder-treasurer, as the case may be, for a term of four (4) years.
(b)
(1) The city council may provide by ordinance for the appointment of the city treasurer.
(2) An ordinance under subdivision (b)(1) of this section shall be passed before the filing period begins for an election for the office of city treasurer, but no later than the February preceding the beginning of the early filing period.