As I can find through the State of New Hampshire's website:

• Article 100, b
  • The general court, by an affirmative vote of a majority of all members of both houses voting separately, may at any time submit the question "Shall there be a convention to amend or revise the constitution?" to the qualified voters of the state. If the question of holding a convention is not submitted to the people at some time during any period of ten years, it shall be submitted by the secretary of state at the general election in the tenth year following the last submission. If a majority of the qualified voters voting on the question of holding a convention approves it, delegates shall be chosen at the next regular general election, or at such earlier time as the legislature may provide, in the same manner and proportion as the representatives to the general court are chosen. The delegates so chosen shall convene at such time as the legislature may direct and may recess from time to time and make such rules for the conduct of their convention as they may determine.

Essentially, unless the General Court with a majority vote in each house calls for a convention, the Secretary of State shall submit to the voters the question of whether or not to host a constitutional convention. The purpose of this being to offer the citizens of New Hampshire to amend their Constitution as needed and, in a sense, force the voters to at least take their key government document under advisement from time to time. If this were approved, at the next general election, the citizens of the state would choose their delegates to send to the convention.

Whether you support the matter or not is entirely of your own decision, but I'll offer you my thoughts as a random internet nobody from New Hampshire.

The average citizen, whether they be from New Hampshire or another state, rarely look at what the State Constitution or their State Statutes say, until such time that they need something to justify their position. Regular reflection on our most crucial documents is healthy and should be encouraged. However, when you consider the environment in which this question is now being posed, it is one of heightened emotions, fears, and hostility. No one can say for certain what would come out of a convention and whether or not there would be dramatic ramifications. I think we would be better off choosing not to hold a convention and instead wait until such time that the waters clear and cooler heads prevail, when there can be a thoughtful and beneficial conversation.

But hey, that's me.