With respect to all customers located within the geographic area in which a water and fire protection authority (“authority”) is authorized by its certificate of incorporation to render water and fire protection service (said customers hereinafter called “county customers”), the board of water and sewer commissioners of a city (“commissioners”) is hereby prohibited from charging said county customers for water service or sanitary sewer service or both, and for the connection fee or fees for such service or services, at a rate or rates or by manner of calculation which exceeds the rate or rates or manner of calculation for the same service or services or connection fees charged by the commissioners to customers located within the city limits, and in all respects in addition to the aforesaid the commissioners shall treat said county customers as if they lived within the city limits.