Abortion is currently legal in NH before the fetus is 24 weeks old. After 24 weeks of age, abortion is illegal with the only exception being medical emergencies and fatal fetal diagnoses. According to an nhpr article published last month.

This article will give you more info on nhs abortion laws and what's being proposed:

https://www.nhpr.org/politics/2023-02-21/how-nh-lawmakers-are-weighing-changes-to-the-states-abortion-laws-post-roe

I will say that NH is ass backwards in that they are currently considering a law that would ban gender affirming care for minors as well as ban teaching about gender identity in schools:

https://www.wmur.com/amp/article/new-hampshire-bill-gender-affirming-care-children/43239700