No, not according to a federal court in Utah (in dicta). The federal Wiretap Act governs intercepts of contemporaneous transmissions.
In a recent case, a confidential informant gave the FBI printed copies of Jones’ sexually explicit emails to a 15 year old girl in Salt Lake City. Jones moved to suppress the email evidence, claiming that the informant violated the Federal Wiretap Act.
The court ruled against Jones, and used this hypothetical: Say Mr. Jones used a public library computer and a librarian discovered the messages. The court said that to violate the Act, the librarian (as informant) would have to intentionally intercept his emails contemporaneous to their transmission.
Moreover, the Act's provision to suppress illegally intercepted evidence applies only to wire and oral communications, not to electronic communications.
For the case, see U.S. v Bryan Vance Jones, or Jones.pdf Case No. 2:04-CR-00510 PGC, U.S. Dist. Court for the District of Utah, Central Division, (Filed April 12, 2005) Memorandum Decision Denying Motion to Compel Under Wiretap Act.
See also Pamela Manson, "Admissible: Utah judge rules peeking at the messages was not illegal," The Salt Lake Tribune posted 4/14/2005
Minow comment: This case did not discuss state law that could come into play (especially absent federal legal process, as in this case). Here, the informant's identity was under seal, and may have had no connection with the library. I believe in most if not all situations, (maybe not Arizona), if a librarian notices someone committing a possible crime, she can tip off the FBI or local law enforcement without releasing the records. The library could then disclose them pursuant to valid legal process (search warrant etc.)