Both inside and out the Washington Legislative Building resembles the nation's Capitol in Washington, D.C. It was built in 1928 and houses the state Senate, House of Representatives, and many executive offices. But unless you are heavily into state politics, you'll be most impressed by the classic architecture and large rotunda.
The building seems quiet most of the time, and it's enjoyable to roam the marble hallways looking at dusty old photographs of long deceased statesmen. If you want a more structured visit there are somewhat interesting tours provided on the hour.