The State Archives has Birth and Death Registers. Registers or returns of births and deaths were recorded by each county auditor prior to 1907 when the functions were transferred to the state. With a few exceptions, before 1891 births and deaths were not recorded by any level of government in Washington.
Birth Registers record names of parents, name of child, date, and birthplace. The Death Registers record name, place, date, and cause of death. Contact the State Archives Regional Branch representing the appropriate county.
The State Library also has these early birth and death registers in its NW Microfilm collection. These microfilm reels cover all counties in Washington State plus the cities of: Bellingham, Everett, Fairhaven, Olympia, Puyallup, Roslyn, and Seattle.
Please note that many births and deaths went unrecorded during this period and that the completeness of these pre-1907 records varies from county to county.