Your husband would need to file a petition for a change in custody. He would need to file that petition in whatever court last had jurisdiction, I would assume that is Connecticut as that is where the child currently resides.
A change in the custodial arrangement is typically based on a substantial change in circumstances. Here, that change could be that the daughter has aged and matured and she has now expressed a desire to reside with her father, in New Hampshire.
As to her age, you are correct in that she is old enough to express her opinion. However, please understand that the judge is not obligated to follow her expressed desires. The judge will certainly listen to what she has to say, but he will not be bound to abide by her requests.
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