Nurses and other UMass Memorial Medical Center staff members who have not been vaccinated against the flu were told this week that they must wear a mask on the job to protect patients from being infected during a hospital stay. Similar or even more stringent policies are in place at some other Massachusetts hospitals, but the change at UMass Memorial has angered some nurses who say the hospital is trying to shame them into getting a flu shot.

“They’re just bullying people,” said Ellen Smith, who works in intensive care at the health system’s university campus. Smith, who was wearing a mask Friday, said she has not gotten a flu shot during 20 years as a nurse.

The state requires hospitals to offer free flu shots. Employees must get one or sign a form declining vaccination. Some hospitals approached 100 percent vaccination rates during the 2011-2012 flu season, taking into account exemptions for medical or religious reasons. The overall state rate for employees at acute care hospitals was about 81 percent.

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UMass Memorial’s vaccination rate was 61 percent, one of the lowest in the state.

“I think we have a lot of people who just have concerns about the vaccines or really, I think, don’t want anyone telling them what to do and have chosen not to get it,” said Dr. Robert Klugman, UMass Memorial chief quality officer. “Nothing is perfect. Flu vaccination isn’t perfect. Masking isn’t perfect. But, they’re the best things known to reduce the risk of spreading infection.”

But the mask “makes your patients afraid of you,” Smith said, and there are no such requirements for visitors to the hospital. She said she would stay home if she were sick to protect her patients, but a person who has the flu can be contagious even before they feel symptoms.

Smith is a union representative for the Massachusetts Nurses Association, which has been protesting staffing cuts at UMass Memorial and is in contract negotiations. The union asked the hospital to consider narrowing the policy to require the masks to be worn only within six feet of patients, but the administration refused, Smith said.

Worker requirements to protect patients are not uncommon in hospitals, Klugman said. Certain nurses and doctors are required to be vaccinated against measles, for example. Most must have an annual tuberculosis test, and everyone is required to wash their hands often.

“We think it’s a reasonable expectation of our staff to meet these requirements [regarding the flu] to protect their patients—and themselves and their families, but primarily we have a duty to our patients,” Klugman said.

Klugman said the Worcester health system’s vaccination rate has risen above 90 percent this year. UMass Memorial mandates vaccination for doctors, licensed independent practitioners, and medical students, while other workers now are given the choice of a shot or a mask.

Some hospitals in the state require all employees to get the shot, if they don’t have a clear exemption. The Massachusetts Hospital Association supports such a policy.

Spokeswomen for Sturdy Memorial and Lawrence General hospitals, two that had near-universal vaccination last year, said they mandate vaccination among those employees who work with patients and require those without a flu shot to wear masks throughout the hospital.