What are my employee rights if I refuse to sign the handbook?

You don't really have any special rights in this instance. If you refuse to sign the handbook, you can not be allowed to begin work (as they've done), or you can likely be terminated for refusing to comply with company policy. You don't state what "illegalities" the handbook might contain, but these facts could alter the scenario significantly, however. It all depends on what the issues are, why you think they're illegal, how they might apply to you, etc. Then, it's also important to keep in mind that signing the employee handbook is usually prefaced somewhere with a clause that states something to the effect of "signing this doesn't have any legal effect, other than that the signed employee is indicating that they've received and read the handbook." If you believe your employer's policy, as outlined in the handbook, is illegal, you should report it to the appropriate authorities.