A spokesman for the hospital, Christian Preston, said Friday that he could not comment on the case because of the litigation and privacy concerns. But he defended the hospital’s record, saying it had a 22-percent C-section rate compared with a state average of 34 percent. Its 2012 rate of “vaginal birth after C-section” was almost 29 percent, much higher than the state average of 11 percent, he said.

The lawsuit, filed last month in State Supreme Court in Brooklyn, where Mrs. Dray lives, also names Dr. Leonid Gorelik, who delivered the baby, as a defendant. Dr. Gorelik, in court papers, denied that he had taken Mrs. Dray for a C-section against her will. He said that her own “culpable conduct and want of care” contributed to any injuries she may have sustained.

Dr. Ducey’s lawyer did not respond to a request for comment. In the medical record, he wrote that the fetus was “at risks for serious harm without the C-section.”

Dr. Howard Minkoff, chairman of obstetrics at Maimonides Medical Center in Brooklyn, whose articles on the subject of patient autonomy have been published in medical journals, said he believed that women had an absolute right to refuse treatment even if it meant the death of an unborn child. “In my worldview, the right to refuse is uncircumscribed,” Dr. Minkoff said, cautioning that he was not commenting on the particular facts of Mrs. Dray’s case. “I don’t have a right to put a knife in your belly ever.”

Such a person might be accused of being immoral or a terrible mother, he said, “but we won’t tie you down.”

As she describes it, Mrs. Dray’s experience illustrates the debate over C-sections.

Now 35, she is the mother of three healthy boys. She found her doctors through word of mouth and the Internet, she said, speaking in the office of her lawyer, Michael Bast. She said the first doctor, at NewYork-Presbyterian/Weill Cornell hospital, began urging her to have a cesarean after her water had broken and she had labored for a few hours. Hoping for a different outcome for her second pregnancy, she went to Lenox Hill Hospital, with the same result.

Still hoping for a vaginal birth, she changed doctors again for the third pregnancy. She also hired a doula to help her with the childbirth.