Nationwide, there is no complete data about how many pregnant women are arrested, jailed or imprisoned each year. However, a recent survey conducted by Johns Hopkins Medicine found that at least 1,400 pregnant women were admitted to federal and 22 state prison systems in 2016 and 2017. New York declined to participate, citing a lack of staff to compile the data, Dr. Sufrin, the lead researcher, said.

Last year, Congress banned shackling in federal prisons and in the custody of the United States Marshals Service. This year, Georgia and Utah joined New York and at least 27 other states in adopting or expanding laws limiting the use of restraints on pregnant inmates. South Carolina is weighing a ban, while Tennessee rejected a similar proposal.

Some of the anti-shackling laws only limit the use of restraints on pregnant women during labor and delivery, while laws like the one in New York prohibit their use during transport at any stage of pregnancy and for several weeks postpartum. Nearly all of the laws make exceptions if a woman is a flight risk or a threat to herself or others.

Michele Goodwin, a chancellor’s professor of law at the University of California, Irvine, said that while the bans were well intentioned, they had been undercut by a lack of accountability that enabled the practice to persist.

“For the most part,” she said, “states that have banned the shackling of pregnant women haven’t bothered to go back and form commissions to see whether or not they are doing so.”

In the Jane Doe case, the attending physicians said in pretrial testimony that they were outraged by the police officers’ actions, and that they later used the case to teach other medical residents how to advocate for patients, one of her lawyers, Katherine Rosenfeld, said.

A lawyer who represented the doctors said it was the hospital’s policy to decline to comment on its cases.