Not the way I read it--if you're talking about a true auto knife, rather than an assisted opener (though I don't know how that distinction holds up in Washington, either).
RCW 9.41.250: Dangerous weapons Penalty.
Every person who...Manufactures, sells, or disposes of or possesses any instrument or weapon of the kind usually known as slung shot, sand club, or metal knuckles, or spring blade knife, or any knife the blade of which is automatically released by a spring mechanism or other mechanical device, or any knife having a blade which opens, or falls, or is ejected into position by the force of gravity, or by an outward, downward, or centrifugal thrust or movement ...is guilty of a gross misdemeanor...