The Connecticut Childbirth & Women’s Center in Danbury is a 50-minute drive from Evelyn DeGraf’s home in Westchester, N.Y. Pregnant with her second child, the 37-year-old didn’t hesitate to make the drive — she wanted her birth to be attended by a midwife, not a doctor. DeGraf believed midwifery care to be more personal and less rushed than that delivered by an obstetrician.