This question comes up most frequently for employees in the health care industry, in which employees are often in close contact with patients who are very young, very old, and who have compromised immune systems from chemotherapy or other treatments. The general answer is yes they can; with a few caveats.
Many health care employees are in unions whose conditions of employment are governed by Collective Bargaining Agreements (“CBAs”). Requiring vaccination could be a change in the terms of the deal and could violate the agreement.
Employees whose religious beliefs do not allow them to be vaccinated could have a complaint under the Connecticut Fair Employment Practices Act or Title VII of the Civil Rights Act, which prohibit discrimination on the basis of religion, if the employer disciplines them for refusing the vaccine.
While both a CBA and religious beliefs could provide a legal reason for employees to refuse a flu shot, the importance of protecting patients can’t be overlooked in the health care industry. The importance of preventing a widespread flu outbreak and further sickening vulnerable patients could be found to be so important that it trumps oher considerations.