Please allow me to add clarifying information. I believe you are referring only to a Non-Resident application from a state that does not issue carry permits. I have checked the Resident application and cannot find this requirement.
For the Non-Resident application the section you refer to appears to be:
“A non-resident pistol license will not be issued unless you supply:
1) A copy (front & back) of your valid concealed carry license issued by the state, county, or town in which
OR IF YOU RESIDE IN A STATE THAT DOES NOT REQUIRE A LICENSE TO CARRY CONCEALED: (Pursuant to Saf-C 2102.03)
2) A letter from your local police department signed by an authorized representative indicating the following:
a) The state does not require a license to carry concealed for residents; b) To the best of the local police departments knowledge, the applicant:
i. Is not a drug user of controlled drugs or narcotics without orders from a physician;
ii. Has not been treated for mental illness, emotional problems, or confined to a mental health facility;
iii. Has no domestic violence petitions that would prevent possession of weapons under federal law; and iv. Has not been arrested or convicted of a misdemeanor domestic violence.”
Clicking on the section referred to (Saf-C 2102.03) and doing a Google search leads you to a letter from the Office of State Legislative Services dated July 18, 2013: https://www.nh.gov/safety/divisions/nhsp/ssb/permitslicensing/documents/Saf-C2100.pdf. I can’t figure out when this change was instituted but appears to change the requirement from Vermont to any state that doesn’t issue a carry permit.
So all I can find is a requirement that your local police chief write such a letter for a Non-Resident applicant from a state that does not issue a carry permit. There is no mention of the Colonel of the NH State Police, nor is there any requirement that I can see for a New Hampshire resident to obtain such a letter from their local police chief.