N.H. Rev. Stat. Ann. § 471-C:31-a

For periods after January 1, 1985, any owner who comes forward to make a claim for assets which have escheated to the state or counties may petition for payment of those assets. Upon receiving sufficient proof of the validity of such owner claim , the administrator shall pay such claim to the owner in accordance with the provisions of this chapter. For funds requested and approved, the governor is authorized to draw a warrant from any money in the treasury not otherwise appropriated.