According to
http://www.mass.gov/dfwele/dfw/wildlife/living/keeping_wildlife.htm
, these are the only mammals allowed:
Lawful (no MassWildlife permit required):
Only the following 11 mammals (or groups) may be kept as pets.
Four-toed (African Pygmy) Hedgehog;
Chinchilla, derived from captive stock;
Deer Mouse and White-footed Mouse;
Degu; Egyptian Spiny Mouse;
House Mouse;
Jerboas;
Norway Rat;
Paca;
Southern Flying Squirrel;
Striped Hamster.
Unlawful: All other mammals not listed as domestic.
Here is the list of domestic mammals:
DOMESTIC MAMMALS:
Domestic dog (for Hybrids, see below)
Mink, propagated in captivity for 2 or more generations (M.G.L. Ch. 128, § 8B)
Domestic ferrets which have been surgically neutered or spayed and rendered incapable of breeding (M.G.L. Ch.131, § 77)
Domestic cat, including the Pixie Bob and Bengal Cat (for Hybrids, see below)
Domestic ass, including mules, burros, and donkeys
Domestic horse
Domestic swine, but not including Wild Boars or free-living wild pigs or swine
Llama
Alpaca
Dromedary Camel
Domestic Water Buffalo or Carabao
Domestic cow
Domestic yak
Zebu cattle
Domestic goat and sheep
Domestic hamster (Golden Hamster)
Guinea Pig
Mongolian Gerbil
Laboratory rat and mouse
Domestic rabbit, but not including so-called "San Juan" rabbits