Persons in any county containing a city of the metropolitan or primary class which has an established city-county or county health department pursuant to sections 71-1626 to 71-1636 which has an established birth and death registration system shall be exempt from the requirements of direct filing of birth and death certificates required by sections 71-604, 71-605, and 71-606. The certificates for the births and deaths occurring in any such county shall be filed with the vital statistics office of the city-county or county health department within five business days of the date of the birth or death. The city-county or county health department shall forward the certificates to the department within ten business days of the date of the birth or death.