When I see a question like this It gets me looking again when I don't have an answer. Got looking in the Admin Rules for ME and found this. It states unless authorized by law and a person with a valid permit is authorized by law. The Terminal Building may be posted and if it is I would not go into the Terminal but from the way I read it it is legal to carry outside the Terminal. Look in Chapter 400 Here:
http://www.maine.gov/sos/cec/rules/17/chaps17.htm
17 DEPARTMENT OF TRANSPORTATION
229 OFFICE OF COMMISSIONER
CHAPTER 400: RULES AND REGULATIONS FOR THE USE OF THE AUGUSTA STATE AIRPORT
SUMMARY: The following rules and regulations govern the administration, operation, and use of the Augusta State Airport.
.01 DEFINITIONS. Unless the context otherwise indicates, the following words when used in any rule or regulation administered by the Maine Department of Transportation, Bureau of Aeronautics shall have the following meanings:
B. Airport. Airport means the Augusta State Airport as it now exists and as it may be expanded in the future, including all lands and roadways.
.08 WEAPONS: FIREARMS: EXPLOSIVES
No person, except those duly authorized by law, shall carry any weapon, firearm, or explosive on the airport, except encased sporting guns for air shipment.