Any city or town may elect to participate in the retirement system established by this chapter: PROVIDED, That a first-class city may establish or maintain any other retirement system authorized by any other law or its charter. The manner of election to participate in a retirement system under this chapter shall be as follows:
(1) The legislative body therein by ordinance making such election;
(2) Approval by vote of the people of an ordinance initiated by the voters making such election;
(3) Approval by vote of the people of an ordinance making such election referended to the people by the legislative body.
Any ordinance providing for participation therein may on petition of the voters be referended to the voters for approval or disapproval.
The referendum or initiative herein provided for shall be exercised under the law relating to legislative initiative or referendum of the particular city or town; and if the city or town be one for which the law does not now provide such initiative or referendum, it shall be exercised in the manner provided for legislative initiative and referendum of cities having a commission form of government under chapter
35.17 RCW, the city or town council performing the duties and functions under that law devolving on the commission. A majority vote in the legislative body or by the electorate shall be sufficient to carry or reject. Whenever any city or town has elected to join the retirement system proper authorities in such city [or town] shall immediately file with the board an application for participation under the conditions included in this chapter on a form approved by the board. In such application the city or town shall agree to make the contributions required of participating cities [or towns] in the manner prescribed herein and shall state which employee group or groups are to originally have membership in the system.
In the case of a state association of cities and towns, election to participate shall be by majority vote of the board of directors of the association.