Unless physical maturation is slowed in New Hampshire for some reason it would be no different in New Hampshire than any other state. Males produce sperm by that age and females have started estrus by the age of 22 so yes, it would be possible.
If you mean; is it legal for people of those ages to engage in coitus, the answer is; in general, yes but there is an exception if the elder is in a position of authority (e.g. Teacher)
The parent of the younger can does have legal means to prohibit the relationship though. Statutory rape is not the only concern in such a relationship.
Mind you, if the younger is 15 when the relationship started and can be proven by the relationship producing a child, the elder can be successfully prosecuted due to that evidence.