The parents of a 3-year-old who died after heart surgery at North Carolina Children’s Hospital in 2016 are suing the institution, saying it failed to disclose internal concerns about the quality of its care.

Tasha and Thomas Jones, the parents, also allege that doctors didn’t warn them about problems with the heart surgery program, and “instead chose to protect their own reputational and monetary interests” by continuing to refer patients to the Chapel Hill hospital, according to a complaint filed on Thursday in North Carolina state court.

In 2016, Skylar Jones underwent was considered a relatively low-risk procedure to repair a heart defect. Soon after leaving the operating room, the girl suffered complications that led to her death two months later at the state-owned hospital, which is affiliated with the University of North Carolina.

At that time, doctors were becoming increasingly troubled that their patients seemed to fare poorly after heart surgery. A New York Times article in May revealed the turmoil, and included secret audio recordings of doctors questioning whether to keep sending patients there.

In one meeting, according to a recording provided to The Times, the head of the hospital told cardiologists to “do what your conscience says,” but also said that reducing surgeries could hurt revenues and lead to job cuts.

According to the lawsuit, doctors at UNC told Skylar’s parents that the hospital offered “state-of-the-art care for pediatric cardiac patients.”

The Joneses filed two claims on Thursday: one in state court, against four doctors; the other with a state commission that hears cases against state-run agencies, including the University of North Carolina health system.

Named in the state complaint were Drs. Kevin Kelly, head of the children’s hospital until his retirement last year; Michael Mill, the surgeon who operated on Skylar; Timothy Hoffman, the chief of pediatric cardiology; and Pamela Ro, a cardiologist.

In meetings in 2016 and 2017, all nine of the hospital’s pediatric cardiologists — who diagnose and treat heart conditions but don’t perform surgeries — expressed concerns about the program’s performance.

Some of them had tried to get mortality data to help decide where to refer patients, but the hospital did not have the information to share at the time, even internally.

This June, after a yearlong legal battle with The Times, the hospital released data showing that its death rate was nearly 50 percent among children with the most complex heart conditions. The data also showed that the hospital’s overall mortality rate for pediatric heart surgery was higher than those of most of the 82 hospitals in the United States that publicly reported such information.

The Joneses’ complaint against the hospital system alleges that its leaders knew the pediatric cardiac surgery program “fell far below acceptable standards, yet UNC systematically failed to disclose this fact to current and potential patients, and failed to take reasonable measures to improve the system.”

After the Times investigation was published, the hospital temporarily suspended its most complex heart surgeries — a measure some doctors had urged years earlier — and introduced an external advisory board and other initiatives to “restore confidence” in the program. That board has since said that the hospital can resume complex surgeries, noting that “significant investment and progress” has been made.

In August, state and federal regulators determined after a monthslong investigation that the hospital was in compliance with federal rules, but “significantly different than it was during 2016-17,” according to a spokesman for the Centers for Medicare and Medicaid Services.

UNC administrators have denied that there were problems affecting patient care in those years, saying only that difficult team dynamics had been resolved by staffing and leadership changes.