Believe it or not, you can open carry in Connecticut, as long as you have a permit.

The permit is a carry permit, open carry or concealed carry.

There was some proposed legislation to restrict open carry, but it did not make it out of committee.

The whole open carry issue came to light about 10 years ago in Connecticut, literally right around the corner from where I work:
Support Is Growing For Openly Carrying Permitted Weapons - tribunedigital-thecourant