Apparently, in most cases, yes.
I was reading this piece at The Atlantic that talks about what your (private sector) employer can and cannot say to you regarding candidates up for election. I must admit that I was a bit taken aback.
From the article:
Can your boss really tell you who to vote for? The answer is probably yes – depending on where you live, and assuming you’re employed in the private sector. In most of the country, there’s little restriction on such communication, legal experts say.Basically, employers have freedom of speech. That means they can say what they want, including strongly suggesting that employees vote for candidates and sending sample ballots to them. Your boss can’t walk into the voting booth with you, and she can’t pay you to vote for a particular candidate, but often there’s little else he or she can’t do.
It seems to me that a secret ballot is just that: a secret. According to this article it appears that employers can try to scare you into voting one way or another. That said, I think that it would be a different story if your boss to come straight out and asked you, “Whom did you vote for?”
Exit question: Can your boss ask you which way you voted? More importantly, if they did ask you this question, how would you reply?