It is perfectly legal to do so as it is not enumerated by RCW 9.41.300 as one of the 5 locations that are legally restricted locations for the carry of firearms. I have been there myself. It is NOT a court or even within the court building. It is NOT a police station or within a police station. It is obviously NOT an airport, jail, or mental health facility. You are free to carry there as long as it's done legally.