N.H. Rev. Stat. Ann. § 566:4

If a power of appointment releasable according to RSA 566:1, or under common law, is or may be exercisable by two or more persons in conjunction with one another or successively, a release or disclaimer of the power, in whole or in part, executed, and delivered or filed, in accordance with RSA 566:2, I, by any one of the donees of the power, shall, subject to RSA 566:2, II, be effective to release or disclaim, to the extent therein provided, all right of such person to exercise or to participate in the exercise of the power, but, unless the instrument creating the power otherwise provides, shall not prevent or limit the exercise or participation in the exercise thereof by the other donee or donees thereof.