Matters most for anyone driving south regularly. Connecticut does not honour a Massachusetts LTC, so without the Connecticut permit a drive to New York or beyond means transport-only through the whole state.
Issued by the Connecticut State Police Special Licensing and Firearms Unit. Massachusetts residents apply as non-residents — you do not need to live in Connecticut.
The 39 State Multi License Course teaches the law for Massachusetts, Maine, New Hampshire, Connecticut, Pennsylvania and Florida in one sitting as the Massachusetts-only class. You then apply for whichever of the six you actually want.

Six states' course requirements, in one visit, for $349 — instead of $1,249+.
Elsewhere on the site: Getting licensed · Massachusetts gun law · Your town · At the range · Who it's for