No, you don't need your birth certificate to register to vote in the NH primaries
Earlier this year, voting rights advocates raised flags about a Republican-led bill making its way through the New Hampshire legislature that would require Granite Staters to show proof of citizenship when they register to vote. (New Hampshire law already requires voters to be US citizens.) And while that legislation passed the state House in March and the Senate in May, it has not gone into effect.
In other words: If you’ve not yet registered to vote in the Sept. 10 state primaries, you can still do so without having to bring along your birth certificate or passport.
Why? Because even though House Bill 1569—which eliminates the existing option for residents to sign a sworn affidavit when registering to vote and instead requires physical proof of US citizenship—sailed through both the House and Senate, the legislation still needs to be signed by the House speaker and Senate president before passed along to Gov. Sununu. As of Wednesday, the bill had still not been signed by Senate President Jeb Bradley, a Republican.
Once signed into law by the governor, the bill would go into effect after 60 days.
https://granitepostnews.com/2024/08/28/no-you-dont-need-your-birth-certificate-to-register-to-vote-in-the-nh-primaries/