Maine and Massachusetts could soon see bans lifted on Sunday hunting Some states are steadily chipping away at longstanding bans on Sunday hunting, and there's a push to overturn the laws in Maine and Massachusetts, the final two states with full bans. Maine’s highest court is considering a lawsuit asking whether the state's 19th century law, which prevents hunting big game animals such as deer, moose and turkeys on Sundays, is still necessary. In Massachusetts, where hunters are also lobbying for Sunday hunting rights, there is a renewed effort to change state laws forbidding the practice. Forty states have no prohibitions on hunting on Sundays.