No. We have a special law in Connecticut to protect this and other similar conduct.

General Statutes § 54-85b(a) provides that "an employer shall not deprive an employee of employment, penalize or threaten or otherwise coerce an employee with respect to employment, because..." that employee participates in a criminal investigation, is subpoenaed to court as a witness in a criminal case, obtains a restraining order or protective order, is the victim of family violence or is as family member of a minor who is a victim of family violence. (See the statute for the exact language).

The remedy is to file a lawsuit in court, but it must be done with 180 days. This is a very short time period for lawsuits in Connecticut generally. You can win damages, reinstatement and a reasonable attorney's fee.