Arenac County was formed from Bay County in 1883, so county records prior to that year may be found in Bay County. Beginning 1883, the State of Michigan required cities and townships to record marriages. Divorces began statewide recording in 1897. All marriage and divorce records more than 100 years old are public records.  MI Division for Vital Records and Health Statistics holds death certificates from 1867 to the present, Arenac County from 1883. For online purchase, the site will send you to VitalChek. Ordering from the county office may be less expensive.