Wash. Rev. Code § 4.84.090
The prevailing party, in addition to allowance for costs, as provided in RCW 4.84.080, shall also be allowed for all necessary disbursements, including the fees of officers allowed by law, the fees of witnesses, the necessary expenses of taking depositions, by commission or otherwise, and the compensation of referees. The court shall allow the prevailing party all service of process charges in case such process was served by a person or persons not an officer or officers. Such service charge shall be the same as is now allowed or shall in the future be allowed as fee and mileage to an officer. The disbursements shall be stated in detail and verified by affidavit, and shall be served on the opposite party or his or her attorney, and filed with the clerk of the court, within ten days after the judgment: PROVIDED, The clerk of the court shall keep a record of all witnesses in attendance upon any civil action, for whom fees are to be claimed, with the number of days in attendance and their mileage, and no fees or mileage for any witness shall be taxed in the cost bill unless they shall have reported their attendance at the close of each day's session to the clerk in attendance at such trial.
RCW 4.84.090
Witness fees and mileage: Chapter 2.40 RCW.