Connecticut's anti-discrimination law prohibits discrimination in employment against any employee who is gay, lesbian or bisexual or who is identifed as being gay, lesbian or bisexual. You do not have to be "out" to be protected. You do not even have to be gay to be protected from discrimination based on sexual orientation. Connecticut is one of about a dozen states that has a statute prohibiting employment discrimination on the basis of sexual orientation and gender identity.
There is no federal law prohibiting such discrimination. There is legislation pending in Congress that would outlaw discrimination on the basis of sexual orientation but not on gender identity.