Each municipality in this State shall adopt by ordinance one of the following alternative methods of nominating candidates for and determining the results of its nonpartisan elections:

(1) The nonpartisan plurality method prescribed in § 5-15-61;

(2) The nonpartisan election and runoff election method prescribed in § 5-15-62;

(3) The nonpartisan primary election and general election method prescribed in § 5-15-63. If nonpartisan elections are not provided for, nomination of candidates for municipal offices may be by party primary, party convention or by petition in accordance with the provisions of this chapter, the applicable provisions of the state election laws and the rules of municipal political party organizations not in conflict therewith.