NEW YORK — A New York doctor who once billed himself as a “world renowned expert” in gynecological cosmetic surgery is facing a manslaughter charge after a patient died following an abortion, an uncommon death that has spurred an even more rare prosecution.

Prosecutors say Dr. Robert Rho punctured his 30-year-old patient’s uterus and cut an artery, then didn’t do enough to keep her from bleeding to death.

The case is one of few criminal cases over a woman’s abortion-related death, and it has put a spotlight on Rho after he had a brush with headlines over an employee’s sexual harassment claim five years ago.

Rho is free on $400,000 bond after pleading not guilty Tuesday. He closed his Queens office shortly after patient Jamie Lee Morales’ July 9 death. No one answered the door Wednesday at his home in Lake Success on Long Island.

His lawyer says Rho has performed 40,000 abortions without any previous problems over a 23-year career, and that prosecutors are overreaching.

“While this is obviously a tragedy, it doesn’t mean that it was a crime,” attorney Jeffrey Lichtman said Wednesday. “This particular doctor does not fit the profile of someone who should be charged with homicide after an alleged botched abortion.”

During his career, Rho built a practice providing gynecological care, abortions and female genital plastic surgery, a service he touted on a now-removed website where he extolled his technique and “natural-looking” results.

State Department of Health records show no disciplinary actions against Rho. Court records show he’s faced an unremarkable number of malpractice suits over the years in a specialty where such suits are common.

At least two of those suits, neither involving abortion, were dismissed. He agreed in May to a not-yet-final $2 million settlement with a patient who said he gave negligent care during a pregnancy that ended with the premature birth of a disabled daughter. Lichtman said Rho maintained he’d done nothing wrong.

Rho also faced suits from a former medical assistant and receptionist who said he groped and sexually harassed them at work. He denied the allegations.

Court records indicate Rho settled with the medical assistant for undisclosed terms. Jurors rejected the ex-receptionist’s harassment claim but found Rho had retaliated against her when he countersued for payment for liposuction he’d performed on her; she said he’d done it to ply her for sexual favors.

Morales came to Rho for an abortion, using her sister’s name, during her second trimester of pregnancy, authorities said.

Queens District Attorney Richard Brown said after Rho sliced Morales’ artery he did another procedure to try to stanch profuse bleeding, but then let her leave, though she’d collapsed and seemed disoriented. She fell unconscious en route to her sister’s home; a hospital gave about six pints of blood but couldn’t save her, prosecutors said.

Rho told health investigators that Morales’ vital signs were stable, she’d stopped bleeding and she was able to walk when she left his office.

Her relatives didn’t respond to messages seeking comment.

A recent study of federal statistics found roughly 1 maternal death per 149,000 abortions nationwide from 1998 to 2010, compared to nearly 9 pregnancy-related deaths per 100,000 live births.

Few physicians face criminal prosecution over such deaths, but some cases are notorious.

Philadelphia doctor Kermit Gosnell was convicted in 2013 of involuntary manslaughter after a patient got a fatal overdose of sedatives during an abortion. He also was convicted of murder for performing extremely late-term abortions where he snipped the spines of infants born alive during the procedures.

In New York City, obstetrician David Benjamin was convicted of murder in 1995 after a patient bled to death from a 3-inch rip in her uterus during an abortion. His license was already in jeopardy from past problems. Prosecutors also said he lied to paramedics to try to cover up — a key factor in charging him, said Brown, who also spearheaded that case.

Rho’s arrest comes in a period of heightened attention to the line between medical error and crime, a question that has gained new momentum amid a rising toll of prescription painkiller overdoses.

Medical groups and malpractice lawyers fear that misjudgment is being criminalized. They note that lawsuits and licensing boards can punish doctors. Some prosecutors question whether that’s punishment enough.

“It’s one thing to be held responsible civilly for the financial penalties, but one of the factors we need to take into consideration is justice for the victims,” says Michael Ramos, the president of the National District Attorneys Association and the DA in San Bernadino County, California.