Here is the email response I got from the State of Maine...
Thank you for contacting the Secretary of State's office. Yes, Maine does register non-resident trailers for non-commercial use. If this is something you are interested in, please contact the Registrations Unit directly at (207) 624-9000 Ext. 52151.
If you have any further questions, please don't hesitate to let me know.
Therese Cahill Low
Director of Constituent Services
Office of the Secretary of State
148 State House Station
Augusta, Maine 04333-0148
Telephone: (207) 626-8400
Fax: (207) 287-8598