N.H. Rev. Stat. Ann. § 491:8

The superior court shall have jurisdiction to enter judgment against the state of New Hampshire founded upon any express or implied contract with the state, including specific performance and other equitable remedies that are not limited to money damages. Any action brought under this section shall be instituted by bill of complaint and shall be tried by the court without a jury. The jurisdiction conferred upon the superior court by this section includes any set-off, claim or demand whatever on the part of the state against any plaintiff commencing an action under this section. The attorney general, upon the presentation of a claim founded upon a judgment against the state, shall submit the claim to the department or agency which entered into the contract, and said department or agency shall manifest said claim for payment from the appropriation under which the contract was entered into; provided, that if there is not sufficient balance in said appropriation, the attorney general shall present said claim to the general court for the requisite appropriation.