Condominium and co-op boards here in New York City have different rules around their voting processes. For some, all votes are secret. Some even use a double-envelope system. In others, there are no systems in place to keep the votes secret. That means that people on the board who collect the ballots aren't prevented from looking at them. They can conceivably retaliate against board members for their votes and even turn other residents against them.
There's no law or regulation that requires New York condo and co-op boards to have secret ballots. Unless there is a confidentiality clause in the bylaws, there's nothing to prevent people from taking a peek and telling others how someone voted on a particular issue, even if the votes are expected to remain secret.
If board members have a concern about their votes being made known to other board members, not to mention their neighbors, there are various steps that they can suggest. Small condos or co-ops may ask either an attorney who represents the board or someone from the management company to handle ballots in order to maintain confidentiality. One Manhattan attorney says that he has done this for boards that he represents.
Condo and co-op boards for larger properties sometimes hire outside professionals to manage their elections. Services like Honest Ballot Association will do that. There's no need to change the building regulations in order to do that.
If your condo or co-op board is having an issue with members' votes being made public and it's causing conflict either among board members or within the building, you may want to consult with your attorney to work out a solution to the problem.
Source: New York Times, "Can Condo Boards Ensure Secret Ballots?," Rhonda Kaysen, Oct. 08, 2016