N.H. Rev. Stat. Ann. § 436:55

The value of all animals directed to be killed by order of the commissioner or his agent shall be first appraised by the owner and the commissioner or his agent. In the event of a disagreement as to the amount of the appraisal, they shall select a third disinterested person to act with them, the expense of said third appraiser being paid by said owner. The value so determined shall be final.