The only residents legally allowed to purchase medical marijuana, as the name suggests, are Maine's medical marijuana patients. To become a patient, you first must receive an MMJ authorization from a state-licensed weed doctor or health professional. Licensed patients can then purchase their medicinal cannabis from designated caregivers or licensed dispensaries.
These MMJ IDs are only available to those who reside in Maine. However, if you have a medical marijuana card from another state, Maine will allow you to purchase medical marijuana so long as you're a current legal patient in a state for which they've approved reciprocity. You can see that list of states on the MMMP's website.