BOSTON – A surgical resident diagnosed this week with an infectious strain of tuberculosis was contagious for six months and may have exposed more than 2,000 patients at hospitals in Boston, Cape Cod and Brockton, public health officials said Thursday.

Hospital officials are contacting patients who came in direct contact with the woman at Boston Medical Center, the VA Boston Health Care System hospital in West Roxbury, Brockton Hospital and Cape Cod hospital. The hospitals also are requiring testing for employees who had close contact with the worker.

Boston Medical Center is requiring 750 of its roughly 4,000 employees to be tested by July 15 or they won’t be allowed to return to work, a hospital spokeswoman said. At least one-third of 3,000 workers at the West Roxbury hospital also will be tested, according to Dr. Michael Charness, the hospital’s chief of staff.

John Rich, medical director at Boston Public Health Commission, which is leading the investigation, said patients have a lower risk of becoming infected than the woman’s co-workers because employees spent more time with her. There is no risk to members of the public who did not have direct contact with the woman, he said.

BPHC spokeswoman Kristin O’Connor said the 1,600 possible exposures in Boston is “a very liberal number.”

“They cast the net wide to identify as many people as possible,” she said.

About 150 patients may have been exposed at Brockton Hospital in December, said hospital spokesman Rich Copp. Roughly 100 to 300 patients may have been exposed at Cape Cod Hospital in January, said spokesman David Reilly.

The woman’s residency at Boston Medical Center had her rotating through the other three hospitals. Last month, she was working at the VA hospital’s facilities in West Roxbury and Jamaica Plain.

Tuberculosis, which usually affects the lungs, can cause weakness, weight loss, fever and night sweats. Dr. Keith Lewis, chief of anesthesiology of BMC, said tuberculosis is “a very treatable disease.”

“The risk to our patients and employees is really very low,” he said.

The worker was showing symptoms in December of a chest infection. That infection wasn’t confirmed until Monday.

“Tuberculosis is very hard to diagnose,” said Sue Etkind, director of the Division of Tuberculosis Prevention and Control at the Massachusetts Department of Public Health. “A number of things could have been causing the same kinds of symptoms.”

Worldwide, tuberculosis kills about 2 million people a year. Antibiotics can cure it, but treatment involves a regimen of up to four different drugs administered for six months. Many strains of tuberculosis also have become resistant to the available drugs.

The worker was diagnosed with an active form of tuberculosis, which means she was contagious and could spread it to other people. However, public officials said 90 percent of tuberculosis infections are latent, meaning patients don’t show symptoms and can’t spread the infection to other people.

Officials said it could be weeks, if not months, before they know whether any other patients or workers have been infected.

BMC and the VA hospital are sending letters and making telephone calls to the 1,600 patients who could have been exposed at the Boston hospitals, as well as offering free tests at a screening clinic from 8 a.m. to 8 p.m. daily.

The hospitals have set up hot lines to answer questions from people fearing exposure. Boston Medical Center: (877) 938-6700; VA Boston West Roxbury: (800) 762-6609; Brockton Hospital: (877) 941-3400; Cape Cod Hospital: (800) 762-6609.