N.H. Rev. Stat. Ann. § 169-D:23

The court and officials in placing children shall, as far as practicable, place them in the care and custody of some individual holding the same religious belief as the child or parents of the said child, or with some association which is controlled by persons of like religious faith. No child under the supervision of any state institution shall be denied the free exercise of his religion or that of his parents, whether living or dead, nor the liberty of worshipping God according thereto.