I also don't believe there are any free standing birth centers in MN, although I think the Long Prarie hospital comes close due to the work of one of the midwives, Ruth. There are two great birthing suites and they are in their own little wing of a very small (under 50 bed, maybe a lot under, I don't remember) hospital. The doctors there are also very friendly toward natural birth. They supported all my choices while I chose to wait almost a full week after my water broke before going into labour with DD.
That said, it is still a hospital, there is still more monitering than I had with my DS at home, there are still nurses who you have never met attending you during labor and birth, etc. Overall though, its a more homey choice than most hospitals.
Mama to three - DD : 1/03, DS 2/06, and DS 6/09.