Wash. Rev. Code § 43.17.050
Each department shall maintain its principal office at the state capital. The director of each department may, with the approval of the governor, establish and maintain branch offices at other places than the state capital for the conduct of one or more of the functions of his or her department.
The governor, in his or her discretion, may require all administrative departments of the state and the appointive officers thereof, other than those created by this chapter, to maintain their principal offices at the state capital in rooms to be furnished by the director of enterprise services.
RCW 43.17.050
Departments to share occupancy-Capital projects surcharge: RCW 43.01.090.
Housing for state offices, departments, and institutions: Chapter 43.82 RCW.