Wash. Rev. Code § 36.75.210
Whenever a county road is established within any county, and such county road crosses the boundary of the county, the board of the county within which the major portion of the road is located may expend the county road fund of such county in laying out, establishing, constructing, altering, repairing, improving, and maintaining that portion of the road lying outside the county, in the manner provided by law for the expenditure of county funds for the construction, alteration, repair, improvement, and maintenance of county roads within the county.
The board of any county may construct, maintain, and operate any county road which forms the boundary line between another county within the state or another county in any other state or which through its meandering crosses such boundary; and acquire by purchase or condemnation any lands or rights within this state, either within or without its county, necessary for such boundary road; and enter into joint contracts with authorities of adjoining counties for the construction, operation, and maintenance of such boundary roads. The power of condemnation herein granted may be exercised jointly by two counties in the manner provided for bridges, or it may be exercised by a single county in the manner authorized by law.
RCW 36.75.210