Wash. Rev. Code § 36.62.120
The first members of the board of trustees of such institution shall be appointed by the county legislative authority within thirty days after the institution has been completed and is ready for operation. The county legislative authority appointing the initial members shall appoint three members for one-year terms, three members for two-year terms, three members for three-year terms, and four members for four-year terms, and until their successors are appointed and qualified, and thereafter their successors shall be appointed for terms of four years and until their successors are appointed and qualified: PROVIDED, That the continuation of a member past the expiration date of the term shall not change the commencement date of the term of the succeeding member. Each term of the initial trustees shall be deemed to commence on the first day of August following the appointment but shall also include the period intervening between the appointment and the first day of August following the appointment.
For an institution which is already in existence on June 7, 1984, the county legislative authority shall appoint within thirty days of June 7, 1984, three additional members for one-year terms, two additional members for two-year terms, and two additional members for three-year terms, and until their successors are appointed and qualified, and thereafter their successors shall be appointed for terms of four years and until their successors are appointed and qualified: PROVIDED FURTHER, That the continuation of an additional member past the expiration date of the term shall not change the commencement date of the term of the succeeding member. Each term of the initial additional members shall be deemed to commence on the first day of August of the year of appointment but shall also include the period intervening between the appointment and the first day of August of the year of the appointment.
Upon expiration of the terms of current members, the successors to current members shall be appointed for four-year terms and until their successors are appointed and qualified: AND PROVIDED FURTHER, That the continuation of a successor to a current member past the expiration date of the term shall not change the commencement date of the term of the succeeding member. Each term of the initial successors to current members shall be deemed to commence on the first day of August following the expiration of a current term but shall also include the period intervening between the appointment and the first day of August of the year of the appointment.
RCW 36.62.120