No, you are not required to attach Form 1040 to your Massachusetts return. The Massachusetts Department of Revenue requires that you attach, with a single staple, all state copies of your forms W-2, W-2G, PWH-WA, 2G and any Forms 1099 showing Massachusetts withholding. If you are making a payment, be sure to enclose Form PV as well.
The New York Department of Revenue does not require you to send a copy of your federal form 1040 either. Please view page 36 in the new York hyperlink for more detailed assembly instructions.