This is open to the public, including, in our experience, access to the Senate floor. The building is gorgeous and at the time we were there, choir singers on the second floor added a zen and beautiful experience to our self tour.
We went because on two previous UWM college tour visits, we never made it inside and honestly, out of things to do that Friday. If I had realized how stunning it is on the inside, and accessible to anyone, I would've made it a first-stop for sure!
Really worth your time, plus some of the best restaurants are right outside so we hopped off to dinner afterwards. (Graft, Graze and Canteen.. pick one)