Wash. Rev. Code § 36.09.050
When a county is divided or the boundary is altered, all taxes levied before the division was made or boundaries changed, must be collected by the officers of the county in which the territory was situated before the division or change. And the auditor or auditors of the county or counties so divided or having boundaries changed, shall apportion the amount of the real property taxes so collected after division or change of boundary to the old county or counties and the new county or counties, in the ratio of the assessed value of such property situated in the territory of each county or counties respectively, and the old county that may have been divided or whose boundaries may have been changed, shall retain all of the personal property taxes on the said tax rolls, as compensation for cost of collection of the entire taxes: PROVIDED, That in such accounting neither county shall be charged with any debt or liability then existing incurred in the purchase of any county property, or in the purchase or construction of any county buildings then in use or under construction, which shall fall within and be retained by the county: PROVIDED FURTHER, That this shall not be construed to affect the rights of creditors: AND PROVIDED FURTHER, That any such county property or buildings shall be the property of and owned by the county wherein the same is situated. In case the auditors of the interested counties are not able to agree upon the proportion to be awarded to each county, the same shall be determined by the judge of the superior court of the district in which all of the interested counties are situated, if they be in one district, and have one common judge, and if not, by the judges sitting en banc of the superior courts of the counties involved. Said auditors shall make said apportionment within sixty days after the creation of any new county or the changing of boundaries of any old county, and if they do not, within said time, agree upon said apportionment, thereafter either or any county affected may petition the judge or judges of any court given jurisdiction by this section, and upon ten days' notice to any other county affected, the same may be brought on for hearing and summarily disposed of by said judge or judges, after allowing each side an opportunity to be heard.
RCW 36.09.050