(IanaL) Generally speaking, in the US, no.
Specifically speaking, if it's done in person, state law holds. In Virginia v Black (2003), the Supreme Court found [1] that states may ban speech which represents a "true threat" (i.e. one whose intent it to cause another party to fear for their lives). But there's generally a high bar and more aimed at allowing regulation of cross burning and neo Nazis than an angry co-worker.
If it's done via the Internet, federal §875 [2] governs. Because of some strange wording and first ammendment concerns, the Supreme Court has held that the intent to actually commit a crime must be present in order for the words to be illegal.
[1] https://caselaw.findlaw.com/us-supreme-court/537/465.html