I think Maine is done by the state, not the local PD.
While you are still a MA resident see how to get a Maine LTC and ask that if you move there can you "convert" it to a resident Maine LTC without taking their class, because the firearms class is done under fed guidelines and should be the same in both states, except parts like in Maine you can not carry in a bar, in Ma. you can. Not the smartest thing to do, but you can.
I know this because my Buddie lives up there and got his LTC last year. Our classes were identical except some of the state rules, like bars.
The courses do not have to follow Federal guidelines. I am sure there are people who teach the course who chose to follow federal guidelines, but it is not required. The course is not subscribed by law. It is pretty much interpreted as any gun safety course. I am sure a MA course is far more stringent than what is required in ME and it will suffice. As far as carrying in Bars... those are limited to Lewston and Portland and the bar must have a sign posted in the entry. All other bars you can.
"(5) Demonstrates to the issuing authority a knowledge of handgun safety. The applicant may fully satisfy this requirement by submitting to the issuing authority, through documentation in accordance with this subparagraph, proof that the applicant has within 5 years prior to the date of application completed a course that included handgun safety offered by or under the supervision of a federal, state, county or municipal law enforcement agency or a firearms instructor certified by a private firearms association recognized as knowledgeable in matters of firearms safety by the issuing authority or by the state in which the course was taken. A course completion certificate or other document, or a photocopy, is sufficient if it recites or otherwise demonstrates that the course meets all of the requirements of this subparagraph.
As an alternative way of fully satisfying this requirement, an applicant may personally demonstrate knowledge of handgun safety to an issuing authority, if the issuing authority is willing to evaluate an applicant's personal demonstration of such knowledge. The issuing authority is not required to offer this 2nd option.
The demonstration of knowledge of handgun safety to the issuing authority may not be required of any applicant who holds a valid State permit to carry a concealed firearm as of April 15, 1990 or of any applicant who was or is in any of the Armed Forces of the United States and has received at least basic firearms training. [1993, c. 524, §8 (AMD); 2005, c. 236, §§3, 4 (REV).]"
Any questions about the law can be researched here:
Title 25: INTERNAL SECURITY AND PUBLIC SAFETY
Part 5: PUBLIC SAFETY
Chapter 252: PERMITS TO CARRY CONCEALED FIREARMS
http://www.mainelegislature.org/legis/Statutes/25/title25sec2003.html