MGL CH 140 Sec 131 (e) 
A Summary of this section in my words..
     After you apply and are fingerprinted at your local police department they have 7 days to forward the information to the State Police Colonel.  Then the state police have 30 days to respond to the Local Police Department with a written eligibility decision.  Then The Local Police Department SHALL within 40 days of your original application approve or deny your application.  The text can be viewed below in the excerpts from the law, or follow the link above to the complete law.

(e) Within seven days of the receipt of a completed application for a license to carry or possess firearms, or renewal of same, the licensing authority shall forward one copy of the application and one copy of the applicant's fingerprints to the colonel of state police, who shall within 30 days advise the licensing authority, in writing, of any disqualifying criminal record of the applicant arising from within or without the commonwealth and whether there is reason to believe that the applicant is disqualified for any of the foregoing reasons from possessing a license to carry or possess firearms. In searching for any disqualifying history of the applicant, the colonel shall utilize, or cause to be utilized, files maintained by the department of probation and statewide and nationwide criminal justice, warrant and protection order information systems and files including, but not limited to, the National Instant Criminal Background Check System. The colonel shall inquire of the commissioner of the department of mental health relative to whether the applicant is disqualified from being so licensed. If the information available to the colonel does not indicate that the possession of a firearm or large capacity firearm by the applicant would be in violation of state or federal law, he shall certify such fact, in writing, to the licensing authority within said 30 day period.

 The licensing authority shall, within 40 days from the date of application, either approve the application and issue the license or deny the application and notify the applicant of the reason for such denial in writing; provided, however, that no such license shall be issued unless the colonel has certified, in writing, that the information available to him does not indicate that the possession of a firearm or large capacity firearm by the applicant would be in violation of state or federal law.