Officially it's not the "capitol building" but "legislative building".
Walter R. Wilder & Harry K. White of NYC were selected as architects of the
Capitol Campus buildings of which the Legislative Building is the centerpiece. Construction began on the Legislative Building in 1922 and was completed in 1928.
The building was damaged by a 6.8 magnitude earthquake hit the Puget Sound February 28, 2001.
At the time of construction, the dome that rises 287 feet above the ground was the 4th tallest dome in the world.