Does any US State require all Ob/Gyn doctors to provide abortions on demand?

I had an ultrasound image made of my heart today at Massachusetts General Hospital. After the procedure, I was talking with the ultrasound operator. The conversation drifted to the subject of church owned businesses being required to provide health insurance including coverage for birth control. The operator acted as if she had not heard of this, but immediately changed the subject.

She claimed that a Ob/Gyn doctor she knew had lost his license to practice medicine because he refused to perform abortions. It sounded strange to me. I know that in a number of states, there isn’t a single doctor who WILL perform an abortion, some because of issues of conscience and others because they don’t want to get shot or car bombed. I tried to Google for states that require all Ob/Gyns to perform abortions in order to retain their medical license. I couldn’t find any. But that doesn’t prove there are none. Does anyone know of such a state, or had this woman been listening to radical right-wing anti-abortion lies?