Wash. Rev. Code § 8.12.360
The clerk of the court in which such judgment is rendered shall certify a copy of the assessment roll and judgment to the treasurer of the city, or if there has been an appeal taken from any part of such judgment, then he or she shall certify such part of the roll and judgment as is not included in such appeal, and the remainder when final judgment is rendered: PROVIDED, That if upon such appeal, the judgment of the superior court shall be affirmed, the assessments on such property as to which appeal has been taken shall bear interest at the same rate and from the same date which other assessments not paid within the time hereafter provided shall bear. Such copy of the assessment roll shall describe the lots, blocks, tracts, parcels of land, or other property assessed, and the respective amounts assessed on each, and shall be sufficient warrant to the city treasurer to collect the assessment therein specified. In no case, however, shall a copy of such assessment roll and judgment be certified to the city treasurer unless and until the awards of the jury shall have first been accepted by the city council or other legislative body as provided by law, or the time for rejecting the same shall have expired.
RCW 8.12.360