29 CFR § 452.97 - Secret ballot.
(a) A prime requisite of elections regulated by title IV is that they be held by secret ballot among the members or in appropriate cases by representatives who themselves have been elected by secret ballot among the members. A secret ballot under the Act is “the expression by ballot, voting machine, or otherwise, but in no event by proxy, of a choice * * * cast in such a manner that the person expressing such choice cannot be identified with the choice expressed.” 47 Secrecy may be assured by the use of voting machines, or, if paper ballots are used, by providing voting booths, partitions, or other physical arrangements permitting privacy for the voter while he is marking his ballot. The ballot must not contain any markings which upon examination would enable one to identify it with the voter. Balloting by mail presents special problems in assuring secrecy. Although no particular method of assuring such secrecy is prescribed, secrecy may be assured by the use of a double envelope system for return of the voted ballots with the necessary voter identification appearing only on the outer envelope.
47 Act, sec. 3(k).
(b) Should any voters be challenged as they are casting their ballots, there should be some means of setting aside the challenged ballots until a decision regarding their validity is reached without compromising the secrecy requirement. For example, each such ballot might be placed in an envelope with the voter's name on the outside. Of course, it would be a violation of the secrecy requirement to open these envelopes and count the ballots one at a time in such a way that each vote could be identified with a voter.
(c) In a mail ballot election, a union may require members to sign the return envelope if the signatures may be used in determining eligibility. However, it would be unreasonable for a union to void an otherwise valid ballot merely because a member printed rather than signed his name if the union does not use the signatures to determine voter eligibility.