Yes, there must be relevant federal statutes about false reporting and perjury etc. since he would have been telling FBI investigators the fake story about the letter (and would have committed some kind of crime by sending the hoax threat letter through the mail, reportedly with some white powder!!). But what can be legally PROVED is different from what we can see is obvious/likely to have happened. Unless Jussie falls apart and confesses (unlikely) he may be able to brazen his way through, or at least disappear into the usual “celebutard rehab” story to recover.
Still the federal aspect may prove to be what really does him in, if he did manage to bring in any serious counter-terrorism investigators with the white powder angle (I recall reading that there was white powder in the hoax letter, although haven’t seen more about that).
Jussie has the I'm a friend of the DNC get out of jail card. It is the real pass from justice.
And yes, I can see some celebrity "rehab" in his future too.