Effective sometime earlier this month it looks like New Hampshire will no longer issue non-resident CCW permits to anyone who does not hold a permit in their own state. The application form for non-resident permits (PDF warning) looks to have been amended recently.
It now states that a non-resident pistol license will not be issued unless you supply a copy (front and back) of your valid concealed carry license issued by the state, county or town in which you reside, or, for states that don't require permits, a letter from the police stating such.
So, if you live in an anti-gun state or jurisdiction where you can't get or don't have a permit, you're now outta luck when it comes to New Hampshire non-resident permits.
In fact, how many states are left that'll issue non-resident permits by mail to out of staters who don't have a permit in their home state? Maine, Virginia, Florida, Connecticut and Arizona are all that come to mind.