Up here there are usually two forms of registration offices. There will usually be one in the offices of the county in which you reside, and there are also independent, state licensed agents (either as part of a dealership operation or as a stand alone business). The agencies are usually more convenient.
Miraculously, last year, the State Patrol dropped their inspection program because it was not cost effective (don't expect this kind of fiscal responsibility from other state and local governments however
). Their primary focus was to snag stolen vehicles with bogus paperwork, caught something like 3 vehicles out of 40,000 the year before.
Assuming your vehicle is titled in California (or any other state for that matter) in your name, the clerk will just copy over the description and VIN as it is currently listed and issue a Washington title.
Welcome to the great NW.