No, neither you nor your boyfriend can be forced to submit to a lie detector "test," and refusing to take it cannot be used against you in a court of law. The only exception might be if either of you is on probation or parole with terms specifying that you must submit to a lie detector test upon demand.

At this point, you would be wise to get a lawyer and refuse the polygraph. You should be able to truthfully say that you're refusing the polygraph based on your lawyer's advice. If your lawyer advises you to take the polygraph, fire him or her and get a more competent lawyer. You have nothing to gain by submitting to this invalid test, and potentially much to lose.

While not specifically related to polygraphs, see these lectures by a law professor and a police interrogator on why you should not speak with police at all without legal counsel, even if you're innocent: