The commissioners of election or the county committee, as the case may be, shall turn over such books to the managers of election of each polling precinct or club, who shall be responsible for the care and custody of such books and the return thereof within three days after such election. The commissioners of election or the county committee, as the case may be, shall return such books to the board of registration prior to the day on which the books of registration are next required by law to be opened by the board of registration and in no event later than twenty days after such election.