In counties having two hundred thousand or more inhabitants, the fiscal year shall begin January 1 and end December 31. Any such county may by an affirmative vote of a majority of all the members of the county board elect to change its fiscal year from a period of twelve months commencing January 1 to a period commencing July 1, and to become subject to all the terms of sections 23-901 to 23-919. Any county hospital operating under sections 23-3501 to 23-3527 may, by an affirmative vote of a majority of the members of the board of trustees of such facility, elect to change its fiscal year to any period of twelve months for determining and carrying on its financial affairs.