The Law
Here are the regulations straight out of the Fish and Game RSA's:

"211:13-b Lead Fishing Sinkers and Jigs; Use Prohibited.
I. No person shall use any lead sinker or lead jig for the taking of fish in any fresh water lake or pond in the state, except as otherweise specifically permitted in this title.
II. A person using any such lead sinker or jig shall be guilty of a violation. Notwithstanding RSA 651:2, the penalty for a violation of this section shall not exceed $250.
III. The prohibition under this section shall apply to interstate lakes and ponds pursuant to RSA 211:14.IV. For purposes of this section, "lead sinker" means any sinker made from lead, the lead portion of which has a mass of one ounce or less, and "lead jig" means a lead weighted hook that measures less than one inch along its longest axis. Lead sinkers and lead jigs shall not include lead fishing related items including but not limited to fishing line, flies, lures, or spoons."