Wash. Rev. Code § 35.58.530
Territory located within a component county that is annexed to a component city after the establishment of a metropolitan municipal corporation shall by such act be annexed to the metropolitan municipal corporation. Territory within a metropolitan municipal corporation may be annexed to a city which is not within such metropolitan municipal corporation in the manner provided by law and in such event either (1) such city may be annexed to such metropolitan municipal corporation by ordinance of the legislative body of the city concurred in by resolution of the metropolitan council, or (2) if such city shall not be so annexed such territory shall remain within the metropolitan municipal corporation unless such city shall by resolution of its legislative body request the withdrawal of such territory subject to any outstanding indebtedness of the metropolitan corporation and the metropolitan council shall by resolution consent to such withdrawal.
Any territory located within a component county that is contiguous to a metropolitan municipal corporation and lying wholly within an incorporated city or town may be annexed to such metropolitan municipal corporation by ordinance of the legislative body of such city or town requesting such annexation concurred in by resolution of the metropolitan council.
Any other territory located within a component county that is adjacent to a metropolitan municipal corporation may be annexed thereto by vote of the qualified electors residing in the territory to be annexed, in the manner provided in this chapter. An election to annex such territory may be called pursuant to a petition or resolution in the following manner:
Any resolution or petition calling for such an election shall describe the boundaries of the territory to be annexed, and state that the annexation of such territory to the metropolitan municipal corporation will be conducive to the welfare and benefit of the persons or property within the metropolitan municipal corporation and within the territory proposed to be annexed.
Upon receipt of such a petition, the auditor shall examine the same and certify to the sufficiency of the signatures thereon. Within thirty days following the receipt of such petition, the auditor shall transmit the same to the metropolitan council, together with his or her certificate as to the sufficiency thereof.
RCW 35.58.530