§ 360. Local veterans' service committees. The same authority which appoints a local director shall appoint for each county and city veterans' service agency a veterans' service committee to assist the local director and shall appoint a chairman thereof. Similar committees may be appointed in each village and town where there is a deputy local director by the mayor of such village and the supervisor of such town in which the branch office of the deputy local director is located or in which it operates. A similar committee may also be appointed in any city in and for which there is not established a separate city veterans' service agency, and in and for which there is a deputy local director and a branch office of the county veterans' service agency; and such appointment in any case shall be made by the city official authorized to appoint a city director in the case of a separate city veterans' service agency.