The right to keep and bear arms does not mean that you can bring a gun into the workplace. A court in Florida recently ruled that a state constitutional right to bear arms did not provide a public policy exception to the “at will employment” doctrine. This means that even though you may have a right to bear arms, your employer may choose to limit this right at the workplace. The court in Florida reached this decision despite the fact that there is a new law in Florida (passed in 2008), which requires employers to allow employees to bring handguns onto the premises provided that they have the proper permit and leave the weapons locked in their vehicles.
Connecticut has no law that requires an employer to allow weapons on their premises. If you have a gun at work in Connecticut, your employer may fire you.