Not sure how it is in Maine, but in New Hampshire a landowner just doesn't need a hunting license. You still need tags. And you can only hunt in season. And if the deer runs off after being hit, leaves your property, and dies somewhere, you're pooched if someone finds it.
Fish and Game have a very fun time making people's lives uncomfortable. Maine Fish and Game is really bad. Its common for them to sit on the shores of lakes with binoculars, have a boat running on standby, see someone catch a fish, and high tail it out there to check licenses. You take out a deer out of season, and they nab you, you're screwed.