§ 2584. Bonds of employees. The board of estimate and apportionment of a city, or in a city having no board of estimate and apportionment, the body or officer performing the duties performed by a board of estimate and apportionment, which may now legally require bonds of employees may continue to require bonds of such employees in such amount as such board of estimate and apportionment or other body or officer shall determine. In all other cities bonds may be required of such employees by the board of education. The premiums on such bonds shall be paid by the city.