1. In all cities of the fourth class, except those in a county of the first class with a charter form of government and which adjoins a city not within a county, the governing body may provide for a primary election, to be held on one of the days specified in section 115.123, only by ordinance. Any city adopting such an ordinance shall file a certified copy thereof with the secretary of state within thirty days of its adoption, and shall not hold a primary election sooner than sixty days after its adoption.

2. In lieu of establishing its own election authority to conduct its primary or general elections, or both, the appropriate election authority of the county in which a fourth class city is located shall conduct such elections. All costs incurred in conducting such primary and general elections, including those incurred by a county election authority under this subsection, shall be paid by the fourth class city for which the elections are held.