No, you do not need a copy of the Death Certificate mailed in. Here is an extract from the MA Form 1 instructions.
"...enclose Form M-1310, Statement of Claimant to Refund Due on Behalf of Deceased Taxpayer, with the refund claimant’s name and Social Security number clearly printed."
The address is: Mass. DOR, PO Box 7000, Boston, MA 02204
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