The law is pretty clear, per the state police link posted above earlier:
Effective October 15, 2015, Public Law 2015, Chapter 327 (LD 652), “An Act To Authorize the Carrying of Concealed Handguns without a Permit,” allows a person who is not otherwise prohibited from possessing a firearm to carry a concealed handgun in the State of Maine without a permit. This law also authorizes a person to possess a loaded pistol or revolver while in a motor vehicle, trailer or other vehicle being hauled by a motor vehicle.
Concealed carry without a permit is limited to people who are 21 or older, with the following exception: If a person is 18 years of age or older, and is on active duty in the Armed Forces of the United States or the National Guard, or has been honorably discharged from the Armed Forces or the National Guard, and is not otherwise prohibited from carrying a firearm, the person may carry a concealed handgun. A person who is 18-20 years old and without the referenced military qualifications must have a permit to carry concealed. The law applies to both residents of Maine and non-residents.