http://legalbeagle.com/7614514-pellet-gun-regulations-massachusetts.html
Pellet Gun Regulations in Massachusetts
By Marguerite Gautier
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Pellet guns, also known as "BB" guns, are air guns that shoot ball bearings. These ball bearings are about the size of a single piece of lead shot in a shotgun shell. The Brady Act under federal law restricts ownership and use of pellet guns in certain circumstances. Some states have also enacted laws regarding pellet guns, one of which is Massachusetts. Its laws pertain to "air guns or BB guns."
Sale or Provision of Pellet Guns to Minors
According to Massachusetts General Law Part IV, Title 1, Chapter 269, Section 12A, no one may sell a pellet gun to a minor under the age of 18. No one who is not his parent, guardian, teacher or instructor may furnish a minor with a pellet gun. The punishment is a fine of not less than $50 nor more than $200 or imprisonment for not more than six months.
Possession by Minors
Section 12B forbids a minor from carrying a pellet gun in any place of public access unless he is accompanied by an adult or has a sporting or hunting license and has a permit from the chief of police of his town of residence granting him the right to carry it. The minor may discharge the gun when accompanied by an adult or when he has a sporting or hunting license.
General Use
No one is allowed to discharge a pellet gun in public areas. Section 12B makes clear that this includes shooting "from or across any street, alley, public way or railroad or railway right of way." Whoever violates Section 12B will be fined not more than $100 and the gun will be confiscated and disposed of by the colonel of the state police.
Looks like most of this is about minors. I couldn't find anything here that would stop an adult from using one on their own property.
I didn't think all "pellet" guns were BB guns either, I guess it depends on your definition. Some air guns shoot a different projectile, some bigger than a BB and are pretty powerful. I'm not sure where these fall in Massachusetts' regulations.