Authority to supervise and maintain any of such recreational facilities and activities may be vested in any existing body or board, or in a public recreation board, as the governing body of any city, town, county or school district may determine. If it is determined that such powers are to be exercised by a public recreation board, such board may be established in any city, town, county or school district and shall possess all the powers and be subject to all the responsibilities of the respective local authorities under this chapter.