There is one freestanding birth center in Missouri. It is about 1.5 hours from Rolla in Columbia. Though it can be a challenge to ride in a car while in labor, I have had quite a few clients who have chosen to birth their babies at this wonderful birth center. My own first baby was born there in 2003 (though, at the time, I lived in Jefferson City, so it was only a 30 minute drive for me).
The birth center is called Columbia Community Birth Center. Phone (573) 447-2700 or visit their website. Phenomenal women. Wonderful place.