Whenever the State Veterinarian or an assistant of his shall, pursuant to § 47-13-360, decide upon the killing of an animal he shall notify the owner of such decision in writing. If satisfactory to the owner three appraisers shall then be chosen in the following manner: One shall be appointed by the State Veterinarian or an assistant of his; one shall be appointed by the owner, and the third shall be the State Veterinarian or an assistant of his. The persons so appointed must be practical stock men and their services shall be rendered free of charge.