Is there a law that says it’s illegal to say a bank is in financial trouble?

The Derogatory Statements About Banks Act makes it a misdemeanor to “willfully and maliciously” make derogatory statements about a bank with the intent “to affect the solvency or financial standing” of the bank. To our knowledge, the law has not been invoked in decades, as it is very difficult to prove the intent of the person making the statement.

Note that the common law of defamation is not subject to the standards in the above law. Banks have brought defamation suits against parties from time to time in recent years, although with varying degrees of success.