Wash. Rev. Code § 36.40.140
When a public emergency, other than such as are specifically described in RCW 36.40.180, and which could not reasonably have been foreseen at the time of making the budget, requires the expenditure of money not provided for in the budget, the board of county commissioners by majority vote of the commissioners at any meeting the time and place of which all the commissioners have had reasonable notice, shall adopt and enter upon its minutes a resolution stating the facts constituting the emergency and the estimated amount of money required to meet it, and shall publish the same, together with a notice that a public hearing thereon will be held at the time and place designated therein, which shall not be less than one week after the date of publication, at which any taxpayer may appear and be heard for or against the expenditure of money for the alleged emergency. The resolution and notice shall be published once in the official county newspaper, or if there is none, in a legal newspaper in the county. Upon the conclusion of the hearing, if the board of county commissioners approves it, an order shall be made and entered upon its official minutes by a majority vote of all the members of the board setting forth the facts constituting the emergency, together with the amount of expenditure authorized, which order, so entered, shall be lawful authorization to expend said amount for such purpose unless a review is applied for within five days thereafter.
RCW 36.40.140