it's a moot point to ask, because New Hampshire isn't going to issue you a CCH permit.
it isn't that simple, where you can just hop in the car and drive over there real quick and pick up a handgun license and then bounce.
there are requirements, just like everywhere else. you have to be a resident, and you have to have proven residency for X amount of time. the Sheriff's Department checks this, of course. you have to have a certification from that state that shows you have completed the necessary classroom course and shooting range requirements. you have to have proper valid identification, drivers license or ID card, issued from that state, which of course originates from actually being a resident there. you cant even submit an application for a CCH permit without the proper ID. and even if you could, you couldn't legally carry without having a license or ID that matches the CCH permit information (address, age, etc.) because of lack of residency, there are several other requirements that you wouldn't meet as a result. for more information visit the state's website
http://www.nh.gov/
have a nice day.