Neb. Rev. Stat. §§ 71-1635
When the county board of any county or counties creates a health department as provided by sections 71-1626 to 71-1636, every other local, municipal, or county public health agency or department, except city or county hospitals, may be abolished, and such county or district health department may be given full control over all health matters in the county or counties, including all municipalities in the county in conformity with the rules, regulations, and policies of the Department of Health and Human Services. When a city has joined in the establishment of a city-county health department, such city-county health department may be given such control over all health matters in the city as may be provided by agreement between the county and the city with the approval of the Department of Health and Human Services. If the health department in a county or city is changed, any lawful ordinance, resolution, regulation, policy, or procedure relating to any of the functions conferred by sections 71-1626 to 71-1636 of the former health department shall remain in full force and effect until it is repealed or replaced or until it conflicts with a subsequently enacted measure.
Neb. Rev. Stat. §§ 71-1635