Wash. Rev. Code § 36.76.110
When the bonds are sold, the money arising therefrom shall be immediately paid into the treasury of the county, and shall be drawn only for the improvement for which they were issued, under the general direction of the board: PROVIDED, That if the improvement includes in whole or in part the constructing or improving of one or more roads, or any part or parts thereof, within the limits of an incorporated city or town, and if the county commissioners find that the amount of the proceeds of the bonds intended to be expended for the improvements within such corporate limits will probably not be sufficient to defray the entire expense of the improvement therein, and if they further find it to be equitable that the city or town should bear the remainder of the expense, they may postpone any expenditure therefor from the proceeds of the bonds until the city or town makes provision by ordinance for proceeding with the improvement within its corporate limits at its own expense insofar as concerns the cost thereof over and above the amount of bond proceeds available therefor.
In such case it shall be lawful for the county commissioners to consent, under such general directions as they shall impose, that the proper authorities of the city or town shall have actual charge of making the proposed improvement within the corporate limits. The city or town shall acquire any needed property or rights and do the work by contract or otherwise in accordance with its charter or ordinances, but the same shall be subject to the approval of the county commissioners insofar as concerns any payment therefor from the proceeds of the bonds.
In such case, as the work progresses and money is needed to pay therefor, the county commissioners shall, from time to time, by proper order, specifying the amount and purpose, direct the county treasurer to turn over to the city or town treasurer such part or parts of the proceeds of the bonds as may be justly applicable to such improvement or part thereof within such city or town, and any money so received by the city or town treasurer shall be inviolably applied to the purpose specified. When that portion of the entire improvement which lies within any such city or town can readily be separated into parts, the procedure authorized by this section may be pursued separately as to any one or more of such parts of the general improvement.
Nothing contained in this section shall be construed to render the county liable for any greater part of the expense of any improvement or part thereof within any city or town than the proper amount of the proceeds of such bonds, or to prevent the city or town from raising any part of the cost of any such improvement or part thereof, over and above the amount arising from the proceeds of the bonds, by assessment upon property benefited, or by contribution from any of its general or special funds in accordance with the provisions of the charter or laws governing such city or town. The provisions of this section, other than the direction for the payment into the county treasury of the money arising from the sale of the bonds, need not be complied with until after the issuance of the bonds and the validity of the bonds shall not be dependent upon such compliance.
RCW 36.76.110