Wash. Rev. Code § 10.46.220
In all convictions for felony, whether capital or punishable by imprisonment in the penitentiary, the clerk of the superior court shall forthwith, after sentence, tax the costs in the case. The cost bill shall be made out in triplicate, and be examined by the prosecuting attorney of the county in which the trial was had. After which the judge of the superior court shall allow and approve such bill or so much thereof, as is allowable by law. The clerk of the superior court shall thereupon, under his or her hand, and under the seal of the court, certify said triplicate cost bills, and shall file one with the papers of cause, and shall transmit one to the administrator for the courts and one to the county auditor of the county in which said felony was committed.
RCW 10.46.220