Wash. Rev. Code § 36.40.100
The estimates of expenditures itemized and classified as required in RCW 36.40.040 and as finally fixed and adopted in detail by the board of county commissioners shall constitute the appropriations for the county for the ensuing fiscal year; and every county official shall be limited in the making of expenditures or the incurring of liabilities to the amount of the detailed appropriation items or classes respectively: PROVIDED, That upon a resolution formally adopted by the board at a regular or special meeting and entered upon the minutes, transfers or revisions within departments, or supplemental appropriations to the budget from unanticipated federal or state funds may be made: PROVIDED FURTHER, That the board shall publish notice of the time and date of the meeting at which the supplemental appropriations resolution will be adopted, and the amount of the appropriation, once each week, for two consecutive weeks prior to the meeting in the official newspaper of the county.
RCW 36.40.100