Petitions, certificates and minutes specified in this article shall be filed in the office of the Board of Elections of the county, except as follows: for an office or position to be voted for wholly within the city of New York, in the office of the Board of Elections of that city; for an office or position to be voted for in a district greater than one county, or portions of two or more counties, in the office of the state board of elections; for a village office to be filled in a village election not conducted by the board of elections, in the office of the village clerk. All such petitions and certificates shall at the time of filing thereof be endorsed by such officer or board with the day, hour and minute of such filing. Such officer or board shall keep a book, which shall be open to public inspection in which shall be entered the times of filing all such petitions and certificates; the names and residences of all candidates named therein; the names and residences of all candidates certified to such officer or board; the title of the office or party position; the name of the party or independent body to which the petition or certificate relates and a memorandum of any objections to such petition or certificate. Forthwith upon the filing of a petition or certificate designating or nominating a person or persons for public office, such officer or board shall mail notice thereof to each such person. Such notice shall also state the last day to decline such designation or nomination, and include a statement that the candidate’s name shall appear on the ballot as it appears in such notice.