N.C. Gen. Stat. § 68-19
If the owner and impounder cannot agree as to the cost of impounding and maintaining such livestock, as well as damages to the impounder caused by such livestock running at large, then such costs and damages shall be determined by three disinterested landowners, one to be selected by the owner of the livestock, one to be selected by the impounder and a third to be selected by the first two. If within 10 days a majority of the landowners so selected cannot agree, or if the owner of the livestock or the impounder fails to make his selection, or if the two selected fail to select a third, then the clerk of superior court of the county where the livestock is impounded shall select a referee. The determination of such costs and damages by the landowners or by the referee shall be final.
N.C. Gen. Stat. § 68-19