A city which has no hospital located therein maintained by the city, shall, when the provisions of sections 44:5-4 to 44:5-7 of this title are assented to by a majority of the electors as hereinafter provided, make and enter into a contract or agreement with any regularly incorporated hospital supported in whole or in part by private subscription and located in the city, to pay to that hospital for a period not exceeding ten years in any one term, a sum equal to one-third of a mill on every dollar of assessable property returned by the assessor of the city, for the purpose of supporting, maintaining and caring for such indigent patients as may be sent to that hospital by order of any city physician, overseer of the poor or other proper authority of the city. Said sections 44:5-4 to 44:5-7 shall not take effect in any city until assented to by a majority of the legal electors thereof voting at any election for municipal officers to be held in the city.