Local government of a town gets its authority from the state legislature. That includes (a) written laws (statutes) passed by the legislature, (b) the New Hampshire Constitution (c) administrative regulations enacted by state agencies and (d) "common law" developed and explained by courts. Basic New Hampshire statues as passed by the legislature are collected in the Revised Statutes Annotated (RSA) and can be accessed at the New Hampshire state government website.
Town Ordinances - State law allows towns to make by-laws (ordinances) voted on at town meetings for "making and ordering their prudential affairs. (See town ordinances link for specific details.)
A town meeting town, like Jackson, is a direct or pure democracy. All general town authority resides in the voters themselves at town meeting, not in any representative body like a town counsel and not in the selectmen. If the town meeting is considered the Legislative body of the town, however, the board of selectmen acts as the town's administrative or managerial body.
One of the roles of the board of selectmen is to act as the advisory body to the town meeting. The advice is given through the selectmen's authority over the Warrant (RSA 39:2) and preparation of the budget (RSA 31:9 and 32:5).
As part of this advisory role, the board of selectmen prepares an annual financial report of the town and is responsible for publishing the reports of all other town officers. This report must be made available 7 days before the annual meeting.
Town Moderator - The moderator controls all annual and special town meetings, but the moderator's declarations must always be subject to being overruled by the voters by a simple majority. (RSA 40:4)
Timing -There is at least one annual meeting the second Tuesday in March (or May if the town so votes). Otherwise a special meeting can be called anytime by the selectmen, or by petition of 50 voters (or 1/4 of the town), whichever is less.
Warrants - The selectmen prepare the warrant for the town meeting and can add any article they wish, right up to the moment the warrant is posted. There are some limits which apply to appropriations. (See RSA 32:5,1)
Petitioned Articles - For annual meetings, petitioned articles presented to the selectmen before the 5th Tuesday prior to the meeting must be added to the warrant if signed by 25 or more voters or 2% of the voters whichever is less, but in no case fewer than 10. Petitioned articles, once they are on the warrant do not have any special status and are enacted, amended or defeated to the same extent as any other warrant articles.