I've searched the boards for a definitive answer to this without luck, so I suspect it's a legal grey area...but here goes.

Our association was organized in 2011.  There are 58 assessed properties served by the association-owned road. There is one resident who refuses to pay annual assessments, arguing that they never signed anything and are not required to pay. 

Our bylaws state:

"...organized as a statutory non-profit road association pursuant to Title 23, Maine Revised Statutes, sections 3101 to 3104."

I'm very new to this but my understanding, passed down from the "old timers" on the board, is that we are incorporated as a non-profit because the association owns the road and is required to pay taxes, hold insurance, etc.

The non-payer's argument is that non-profit incorporated road associations require a signed agreement from participants and have no power to collect from non-signers.

Can we be a Statutory association under Title 23 sections 3101-3106 while still being incorporated as a non-profit, and thereby retain the authority to collect maintenance fees without a signed agreement?

Your wisdom and experience will be much appreciated.

I think the real question here is whether or not your association has complied with the requirements of 23 MRS sections 3101-3104.  Yes, you can be both a statutory and a non-profit at the same time, and if you are, you have all the powers of a statutory association.  So the question is, when your association was formed, did you go through the process required by section 3101?  Did three or more landowners get a Notary to call the first meeting?  And have you followed the rules since then for notifying members of meetings, coming up with a formula for dues assessments, sending out the result of the votes, etc?  If you have, then you should be all set.  But as the attorneys at our annual conference always remind us, if someone tries to sue you (or if you sue them,) their attorney is going to look for any requirement of the law that you may not have followed to the letter, and use that to say that you are therefore not a legitimate statutory road association.

I am curious about the phrase you used 

 we are incorporated as a non-profit because the association owns the road and is required to pay taxes, hold insurance, etc.

If you "own the road" I am wondering if you researched the registry of deeds to see if there is a covenant, similar to condo's.  In the covenant, it would state the owners responsibilities to pay the association dues. Whereas for private roads, owners "share" the road, would have written in their deed that they need to maintain the right of way... 

There was in very olden days a voluntary agreement put on people's deeds to maintain the road (which the owner would sign) and it used to be considered an informal method to repair the roads.  If you go to the resource page, under the DEP's forming an association, you'll see Informal Organization by Signed Agreement.

Welcome to the world of road associations. You on a good start by connecting with MARA.