Gotta have a drivers mirror:
And this kind of seems like a "catch all" about the doors, idk:
But you can fold down the windscreen and wear a motorcycle helmet:
Your local municipality may have codes about it, too.
And this guy http://apps.leg.wa.gov/wac/default.aspx?cite=204-10-022
says you have to be able to positively latch the doors and be able to open from inside or outside but doesn't say you have to have em, either.
I believe you could argue (sucessfully) that at the "time of original manufacture" the doors were intended to be removed, and thus do not violate any written law of the State of Washigton. But then again, you wouldn't be glad to win the arguement; that means you were stopped and cited, then had to appear.