Her treatment by the officers defied a consensus among professional groups like the American Medical Association and the American College of Obstetricians and Gynecologists that using restraints like handcuffs, shackles and belly chains on pregnant women can cause complications and may interfere with doctors’ efforts to treat them, according to the complaint.

The National Commission on Correctional Health Care, which accredits correctional facilities, strongly opposes the use of restraints during labor and delivery and discourages their use during the prepartum and postpartum periods, except when there is an imminent risk that the woman will flee or cause harm.

Following the 6:14 a.m. delivery, a doctor wrote in hospital notes that officers, when informed that state law prevented shackling, said “the N.Y.P.D. Patrol Guide supersedes this law and that patient would need to remain restrained during remainder of hospitalization.”

The guide, which is the official manual of police protocol, requires officers to handcuff and shackle arrestees who require medical or psychiatric attention, but it permits officers to remove the restraints when doctors request it and after consulting with a patrol supervisor. The officers at the hospital did consult a sergeant after the woman and her doctors asked them to remove the shackles, but the sergeant said the restraints were required, the complaint states.

The number of women in the nation’s jails and prisons has grown considerably since the 1980s, which has forced law enforcement and correctional authorities, as well as policymakers, to grapple with the impact of incarceration on women, including those who are pregnant and give birth in custody.

Dr. Carolyn Sufrin, an assistant professor in gynecology and obstetrics at Johns Hopkins Medicine, said a lack of comprehensive data about pregnant women in jails and prisons makes it difficult to study their experiences. “The people who don’t count, don’t get counted,” she said.

New York is one of 26 states that prohibit shackling women in labor, Dr. Sufrin said, and some go as far as banning restraints for all pregnant women in custody. In the other 24 states, no state or federal law limits the practice, she said.