Wash. Rev. Code § 47.52.150
Upon request for a hearing before the board by any county, city, or town, a board consisting of five members shall be appointed as follows: The mayor or the county commissioners, as the case may be shall appoint two members of the board, of which one shall be a duly elected official of the city, county, or legislative district, except that of the legislative body of the county, city, or town requesting the hearing, subject to confirmation by the legislative body of the city or town; the secretary of transportation shall appoint two members of the board; and one member shall be selected by the four members thus appointed. Such fifth member shall be a licensed civil engineer or a recognized professional city or town planner, who shall be chair of the board. In the case both the county and an included city or town request a hearing, the board shall consist of nine members appointed as follows: The mayor and the county commission shall each appoint two members from the elective officials of their respective jurisdictions, and of the four thus selected no more than two thereof may be members of a legislative body of the county, city, or town. The secretary of transportation shall appoint four members of the board. One member shall be selected by the members thus selected, and such ninth member shall be a licensed civil engineer or a recognized city or town planner, who shall be chair of the board. Such boards as are provided by this section shall be appointed within thirty days after the receipt of such a request by the secretary. In the event the secretary or a county, city, or town shall not appoint members of the board or members thus appointed fail to appoint a fifth or ninth member of the board, as the case may be, either the secretary or the county, city, or town may apply to the superior court of the county in which the county, city, or town is situated to appoint the member or members of the board in accordance with the provisions of this chapter.
RCW 47.52.150