Wash. Rev. Code § 10.88.310
The officer or persons executing the governor's warrant of arrest, or the agent of the demanding state to whom the prisoner may have been delivered may, when necessary, confine the prisoner in the jail of any county or city through which he or she may pass; and the keeper of such jail must receive and safely keep the prisoner until the officer or person having charge of him or her is ready to proceed on his or her route, such officer or person being chargeable with the expense of keeping.
The officer or agent of a demanding state to whom a prisoner may have been delivered following extradition proceedings in another state, or to whom a prisoner may have been delivered after waiving extradition in such other state, and who is passing through this state with such a prisoner for the purpose of immediately returning such prisoner to the demanding state may, when necessary, confine the prisoner in the jail of any county or city through which he or she may pass; and the keeper of such jail must receive and safely keep the prisoner until the officer or agent having charge of him or her is ready to proceed on his or her route, such officer or agent, however, being chargeable with the expense of keeping: PROVIDED, HOWEVER, That such officer or agent shall produce and show to the keeper of such jail satisfactory written evidence of the fact that he or she is actually transporting such prisoner to the demanding state after a requisition by the executive authority of such demanding state. Such prisoner shall not be entitled to demand a new requisition while in this state.
RCW 10.88.310