Arizona never had a state capitol building as such. The charming building at the end of Washington Street topped by a copper rotunda was opened in 1901. It was the territorial capitol. Designed by San Antonio architect James Riely Gordon, it was intended to convey the sense that Arizona was ready for statehood (which happened in 1912).
Gordon wanted a much larger building, with a more prominent rotunda and wings for both houses of the Legislature on each side of the building. Yet problems with funding meant the project had to be cut back in size with the massive segments for the Legislature discarded.
In 1918 and 1938, the building was expanded to the west employing the same architecture as the original territorial capitol. Some of the later construction was done by Del Webb's company. It increased the total square footage from the original 40,000 to a final 123,000.
It was home to the Legislature until 1960, when the current House and Senate buildings were constructed, and the offices of the governor, secretary of state, and attorney general until 1974.
In that year, the Brutalist Executive Tower was built (Brutalist is not a pejorative but rather a style in the architectural vernacular; it still has its champions) which now looms over the original capitol, which has been turned into a museum. The AG's office was consigned to a long, unworkable building on Washington east of the capitol before moving to Central Avenue.