In each city and in each county of the state, there is created a public body corporate and politic to be known as the “housing authority” of the city or county, as the case may be. Such authority may not transact any business nor exercise any powers granted by this chapter until the governing body of the city or of the county, as the case may be, by proper resolution, declares that there is need for an authority to function in such city or county. The determination as to whether there is such need may be made by the governing body on its own motion and must be made upon filing of a petition signed by twenty-five residents of the city or county, as the case may be, asserting that there is need for such authority to function in such city or county and requesting that the governing body so declare.