In all cities, unless otherwise provided by law, any person entitled to vote at city elections who is registered on the revised registry list last completed, and any person having a legal right to vote at such elections whose name is entered on a copy of such list before voting, may vote therein in the district for which such registry list is made; provided those persons may vote whose names are restored to the list under the provisions of § 9-42 or whose names are added on the last week day before a regular election under the provisions of § 9-17. Each person so registered shall be permitted to vote, unless he has lost his right by removal from such city since he has registered or by conviction of a disfranchising crime. Any person offering so to vote, and being challenged as to his identity or residence, shall, before he votes, prove his identity with the person on whose name he offers to vote or his bona fide residence in such city, as the case may be, by the testimony, under oath, of at least one other elector or by such other evidence acceptable to the moderator. The names of those voting shall be checked on such copy of such list, and such copy so checked shall be kept on file in the office of the town clerk, as in the case of state elections.