Health officials cited three Massachusetts hospitals in the past six months for wrongly sending away patients from their emergency rooms, in one case resulting in the death of a patient while en route to another facility.

In that episode, caregivers at Charlton Memorial Hospital in Fall River failed to provide needed medical treatment before transferring the patient, who was unstable and in respiratory distress, state investigators concluded.

In a case at St. Vincent Hospital in Worcester, an on-call surgeon refused to come in late at night to perform an emergency operation on a patient with flesh-eating bacteria, investigators found. The patient was transferred to another hospital, and the surgeon no longer operates on patients at St. Vincent, hospital officials said.

Hospitals that break federal rules ensuring public access to emergency services can face especially tough sanctions. Flagrant or repeat violators risk losing their right to treat Medicare and Medicaid patients, which can cost a hospital millions of dollars.

Charlton, St. Vincent, and Lahey Clinic in Burlington - which turned away an emergency room patient in November - have been told they will not lose their Medicare contracts, but they could be fined. Federal officials said it is unusual to have three cases in such a short span.

“It’s the very basic tenet of what we’re all about in health care,’’ said Dr. Mary Anna Sullivan, chief quality and safety officer at Lahey. “You take care of the patient who presents in the ED. End of story.’’