CHICAGO — Patients can refuse a flu shot. Should doctors and nurses have that right, too? That is the thorny question surfacing as U.S. hospitals increasingly crack down on employees who won’t get flu shots, with some workers losing their jobs over their refusal.

“Where does it say that I am no longer a patient if I’m a nurse,” wondered Carrie Calhoun, a longtime critical care nurse in suburban Chicago who was fired last month after she refused a flu shot.

Hospitals’ get-tougher measures coincide with an earlier-than-usual flu season hitting harder than in recent mild seasons. Flu is widespread in most states, and at least 20 children have died.

Most doctors and nurses do get flu shots. But in the past two months, at least 15 nurses and other hospital staffers in four states have been fired for refusing, and several others have resigned, according to affected workers, hospital authorities and published reports.

Dr. Carolyn Bridges, associate director for adult immunization at the federal Centers for Disease Control and Prevention, says the strongest evidence is from studies in nursing homes, linking flu vaccination among health care workers with fewer patient deaths from all causes.

“We would all like to see stronger data,” she said. But other evidence shows flu vaccination “significantly decreases” flu cases, she said. “It should work the same in a health care worker versus somebody out in the community.”