According to handgunlaw.us there is NO acceptance or reciprocity either way between NH and CT. You must get a CT permit if you want to carry there. (or vice versa).
I'm guessing uscarry.com is wrong. There is typically no way in hell a more communist state will ever honor a permit from a state that is less communist than it
is. (this is a general rule). Further, most of the communist states are "landlocked" WRT CCWs. (The PDF on handgunlaw.us says that CT honors NO permits from
any other state, although a handful of them honor the CT permit, but none of them are in this half of the country. )
-Mike