N.H. Rev. Stat. Ann. § 154:11

The selectmen, aldermen or council, on application, shall appraise the damage done to any building or thing by order of the firewards, engineers, or fire officer-in-charge and may assess a tax for the payment therefor, and may make compensation to the owner, unless it shall appear that the fire began in such building, or that the same must have been burned if it had not been destroyed or removed.