Here's the link you might find helpful (you should be able to search for your case on that website as well):
http://dw.courts.wa.gov/index.cfm?fa=home.resources
Also, WA state is too broad a notion in terms of specific rules - you want the specific court and get the information from the specific court by calling them or perhaps it's even available on the court's website.
I think that for the traffic case I just got closed, the appeal process at the local district court was to be taken within either 10, 14, or 30 days (don't remember, but it was very short).

