(b) Any public board or officer of a city now exercising health functions may, with the approval of the mayor, contract with the board of managers or other governing authority of any laboratory for the purpose of cooperation and to join and share facilities. 2. If it is the intention of the common council or similar authority of a city to apply for state aid for a proposed laboratory, under the provisions of section six hundred twenty to six hundred twenty-three, inclusive, of this chapter, the common council or similar authority with the approval of the board of estimate, if such exists, shall have the power to establish a laboratory in such city.