Wash. Rev. Code § 36.93.063
The executive of the county shall make the appointments under RCW 36.93.051 and 36.93.061 for the county, if one exists, or otherwise the county legislative authority shall make the appointments for the county.
The mayors of all cities and towns in the county shall meet on or before the last day of January in each odd-numbered year to make such appointments for terms to commence on the first day of February in that year. The date of the meeting shall be called by the mayor of the largest city or town in the county, and the mayor of the largest city or town in the county who attends the meeting shall preside over the meeting. Selection of each appointee shall be by simple majority vote of those mayors who attend the meeting.
Any special district in the county may nominate a person to be appointed to the board on or before the last day of January in each odd-numbered year that the term for this position expires. The board shall make its appointment of a nominee or nominees from the special districts during the month of February following the date by which such nominations are required to be made.
The county appointing authority and the mayors of cities and towns within the county shall make their initial appointments for newly created boards within sixty days of the creation of the board or shall make sufficient additional appointments to increase a five-member board to an eleven-member board within sixty days of the date the county obtains a population of one million or more. The board shall make its initial appointment or appointments of board members from the nominees of special districts located within the county within ninety days of the creation of the board or shall make an additional appointment of a board member from the nominees of special districts located within the county within ninety days of the date the county obtains a population of one million or more.
The term of office for all appointees other than the appointee from the special districts shall commence on the first day of February in the year in which the term is to commence. The term of office for the appointee from nominees of special districts shall commence on the first day of March in the year in which the term is to commence.
Vacancies on the board shall be filled by appointment of a person to serve the remainder of the term in the same manner that the person whose position is vacant was filled.
RCW 36.93.063
Purpose-Captions not law-1991 c 363: See notes following RCW 2.32.180.