RCW 84.44.080

The owner of personal property removing from one county to another between the first day of January and the first day of July shall be assessed in either in which he or she is first called upon by the assessor. The owner of personal property moving into this state from another state between the first day of January and the first day of July shall list the property owned by him or her on the first day of January of such year in the county in which he or she resides: PROVIDED, That if such person has been assessed and can make it appear to the assessor that he or she is held for the tax of the current year on the property in another state or county, he or she shall not be again assessed for such year.