The provisions of section 423.37 shall apply to and bind any city of the third class which by a resolution of its governing body, adopted by a majority of the members thereof shall choose to be bound by it, and such city may thereafter continue to be bound by it notwithstanding a subsequent change in the classification of the city; but section 423.37 does not apply to any police officers' relief association in existence April 29, 1947 unless the association elects to come under its provisions as herein provided.