Under 220 CMR 25, utilities cannot shut off heat to certain qualified households between November 15 and March 15. This year, according to their press release, "the Massachusetts Department of Public Utilities (DPU) has asked each of the state’s electric and natural gas companies to extend until May 1 the current moratorium on winter utility shut-offs."
This extension is voluntary, however, and while in previous years all utilities have complied with the request, they are under no obligation to do so. You should check with your utility or the DPU to determine whether your utility has agreed to the deadline extension. According to the DPU Legal Division, "so far, two major companies, KeySpan (including National Grid) and NSTAR have agreed to extend the moratorium."
More information on winter heating help and other heating requirements is available at Mass. Law About Winter Heating.