Is it illegal for a supervisor to disclose information about a employee to another employer?

I assume you are referring to a situation wherein your former/current employer is contacting an prospective employer regarding employment for you. In such a s case, generally speaking, there is no legal recourse that can be taken against a former employer for a negative response to a prospective employer's inquiry. With respect to pre-employment inquiries and answers, the law provides a "qualified privilege". Therefore, employers (past/present) will be free to answer such questions honestly without fear of a lawsuit. Accordingly, a former employee can only sue for willful or reckless remarks that are totally and grossly untrue.

Further, even without the privilege certain statements are legally permissable. For example, statements of fact are not actionable. Therefore, if your past employer says that it would not re-hire you can't sue for defamation since that employer can prove that it's true. Additionally, statements of opinion aren't a basis for a lawsuit. Accordingly, if your past employer said, "X drinks to excess" that is a statement of fact that may be actionable. However, stating that, "I think X is the worst worker I've ever hd to supervise" is a statement of opinion that is not actionable.