(C) The animal control officer, in conjunction with the health department, shall arrange for the supervised confinement of any dog or cat which has bitten a person. The confinement may be on the premises of the owner if the owner will sign a DHEC agreement assuming total responsibility for the safe confinement of the pet or other animal or the confinement may be at the county animal shelter with the current impoundment and boarding fees charged, or the dog or cat may be confined at a private animal shelter or a veterinary hospital at the owner's expense;