The commissioners of election or the county committee, as the case may be, shall turn over registration books to the election managers of each polling precinct, who are responsible for the care and custody of these books and the return of them within three days after the election. The commissioners of election or the county committee, as the case may be, shall return the books to the board of registration before the day on which the books of registration are next required by law to be opened by the board of registration and not later than twenty days after the election.