N.H. Rev. Stat. Ann. § 371:13

If the owner's damages are reduced upon appeal, the public utility shall have judgment and execution against him for the amount of such reduction and costs if he has taken the damages tendered to him; but, if he has not taken such damages, the public utility may retain the amount of such reduction and costs from the tender, or, if the damages have been paid to the state treasurer, the public utility shall be entitled to have such reduction and costs returned by the treasurer.