Wash. Rev. Code § 36.64.010
If the county seat of a county is in an incorporated city, the county and city may contract, one with the other, for the joint purchase, acquisition, leasing, ownership, control, and disposition of land and other property suitable as a site for a county courthouse and city hall and for the joint construction, ownership, control, and disposition of a building or buildings thereon for the use by such county and city as a county courthouse and city hall. Any county or city owning a site or any interest therein, or a site with buildings thereon, may, upon such terms as appear fair and just to the board of county commissioners of such county and to the legislative body of such city, contract with reference to the joint ownership, acquisition, leasing, control, improvement, and occupation of such property.
RCW 36.64.010