This website about laws concludes that given there's no specific NH law against it, it's legal. https://www.neonlaws.com/new-hampshire/

Is it removable, though? Laws do change, so it'd suck for you to make a permanent change only to have them outlaw it while you own the car. I mean, I've seen cars with purple underglow and it is distracting, which does make me wonder if it'll be cracked down on...anyway, if it's removable, you're better off.