The Caveat is in "public way".
The Select Boards do not not have jurisdiction on "state" roads, as opposed to "town" roads.
Neither, have jurisdiction on private roads.
Judging from the comment about neighborhood and summer homes, if the road is part of an Association (e.g., an HOA) the elected Directors of that Association have the jurisdiction to make rules for the road, presuming the owners have not voted otherwise.
Also,
http://www.gencourt.state.nh.us/rsa/...VIII-215-C.htm