When I last looked at the application for a non-resident NH carry permit, there were a few requirements:
--applicants must supply a copy of a carry permit from either their home state, or from another state that issued them such a carry permit
--applicants must consent to a release of information regarding fitness to carry a firearm by their employer(s), chief of police, etc.
I have a problem with my local police department (here in NJ) knowing if I have applied for a carry permit in New Hampshire. Not that they could deny me, but quite frankly, I don't think it's any of their business, and they would keep a record of it in my "file." (For those who are unaware, all law-abiding gun owners have a file, which contain their personal references, employer information, firearms id approval, carry permits (if granted), and registration records of handguns).
I also have a problem with my employer being involved. My employer has been contacted by my police department in the past, and they would keep silent, delaying the process for my firearms id card from being approved, as well as subsequent pistol purchase permits. My employer's (unofficial) policy is to forward any such communications to the legal department, who simply takes the requests and throws them away. My personal supervisors have also in the past used this as leverage against me (though now they know not to, since I attempted litigation against them recently).
You can review the NH permit application here:
Link Removed
As far as I know, a Utah permit requires the applicant to complete a course from an instructor approved by Utah State Police. I don't know of anyone that has that kind of certification.
I have a Florida permit. A Florida permit only requires proof of firearms training. It's more expensive, but easier to get.