All marriages taking place within the state, all divorces, dissolutions, and annulments of marriages decreed by a court of this state, and all corrections of certificates of marriage shall be registered with the office of vital statistics of the department of health. On or before the tenth day of each month, the probate judge of each county shall forward to the department on a form prescribed and furnished by the director of health a certified abstract of each marriage record made by the probate judge during the preceding month.

The clerk of the court of common pleas, on or before the tenth day of each month, shall send to the department on a form to be prescribed and furnished by the director a certified abstract of all decrees of divorce, dissolution, and annulment of marriage and orders correcting certificates of marriage that the clerk recorded during the preceding month. The office of vital statistics shall record and index all records received under this section.