NH has laws (RSA) and administrative rules. The rules have the force of law but are written more or less by the adminstration to implement the laws written by the legislators.
So in this bunch of rules:
http://www.gencourt.state.nh.us/rules/saf-c400.html
I found this:
(c) If the person desiring the single mooring is not the owner of shorefront property, the owner of shorefront property allowing access to the mooring shall file the application, form DSSS 18, on behalf of that person.
So really only shorefront property owners can apply for moorings, but they can allow someone else to install and use them. But they can't rent or sell them.