Wash. Rev. Code § 29A.72.180
If the secretary of state refuses to file an initiative or referendum petition when submitted for filing, the persons submitting it for filing may, within ten days after the refusal, apply to the superior court of Thurston county for an order requiring the secretary of state to bring the petitions before the court, and for a writ of mandate to compel the secretary of state to file it. The application takes precedence over other cases and matters and must be speedily heard and determined.
If the court issues the citation, and determines that the petition is legal in form and apparently contains the requisite number of signatures and was submitted for filing within the time prescribed in the Constitution, it shall issue its mandate requiring the secretary of state to file it as of the date of submission for filing.
The decision of the superior court granting a writ of mandate is final.
RCW 29A.72.180
Initiative, referendum, time for filing: State Constitution Art. 2 s 1 (a) and (d) (Amendment 7).