Wash. Rev. Code § 16.04.030
If the owner or person having such animals in charge fails or refuses to pay the damages done by such animals, and the costs, or give satisfactory security for the same within twenty-four hours from the time the notice was served, if served personally, or in case of horses, mares, mules and asses, within twenty-four hours from the time such notice was posted, if served by posting the same, and in case of cattle, goats, sheep and swine within ten days from the time of such posting, the person damaged may commence a suit, before any court having jurisdiction thereof, against the owner of such animals, or against the persons having the same in charge, or possession, when the trespass was committed, if known; and if unknown the defendant shall be designated as John Doe, and the proceedings shall be the same in all respects as in other civil actions, except as modified in RCW 16.04.010 through 16.04.070. If such suit is commenced in superior court the summons shall require the defendant to appear within five days from the date of service of such summons, if served personally.
RCW 16.04.030