Wash. Rev. Code § 16.08.020
It shall be lawful for any person who shall see any dog or dogs chasing, biting, injuring or killing any sheep, swine or other domestic animal, including poultry, belonging to such person, on any real property owned or leased by, or under the control of, such person, or on any public highway, to kill such dog or dogs, and it shall be the duty of the owner or keeper of any dog or dogs so found chasing, biting or injuring any domestic animal, including poultry, upon being notified of that fact by the owner of such domestic animals or poultry, to thereafter keep such dog or dogs in leash or confined upon the premises of the owner or keeper thereof, and in case any such owner or keeper of a dog or dogs shall fail or neglect to comply with the provisions of this section, it shall be lawful for the owner of such domestic animals or poultry to kill such dog or dogs found running at large.
RCW 16.08.020