The policy states "visible tattoos could pose a threat to safety and security." It says the body art also impairs the officer's "impartial and professional appearance."
Joe Gaetano, president of the marshal's union, tells the Stamford Advocate he can't imagine how a tattoo is a security issue.
Some of the marshals' tattoos signify their military service.
One female marshal has a pink ribbon tattoo to mark her successful battle with breast cancer.
Gaetano said the union has filed a protest with the state Judicial Branch.