My dad read this a long time ago (unfortunately, he can't remember the source) and has been looking for something to back this up for a long time (I've looked some too). I asked this about 3 months ago with no response, so I thought I might as well try again. Thanks for your help!
This inspired me to consult an article that explores the possible Greco-Roman background of the supposed custom referred to during the trial of Jesus in the New Testament gospels, where a prisoner is set free during Passover. (The article is R. L. Merritt, "Jesus, Barabbas, and the Paschal Pardon," JBL 104 (1985), 57–68.). The author mentions several Greek (and Roman) festivals where prisoners are released – the Athenian Greater Dionysia, the Thesmophoria, the Panathenaea, the Lectisternium, etc. However, there were conditions for this release. For one, it was often simply temporary: "merely a parole for the duration of the festival and not an amnesty."
There are a couple of other things mentioned in that article that are somewhat close to what you ask about. The first is that
Lewis Richard Farnell speculates that the original idea which suggested the practice of releasing prisoners may have been that "law and order could be suspended during a short period of license which was especially common at ceremonies connected with the crops."
The second thing is found in a discussion of the festival Kronia. I quote the author at length:
The Greek festival of Kronia had its counterpart in Roman Saturnalia festivals (December 17-23), at which, according to Jane Ellen Harrison, there was also a custom "of releasing prisoners and slaves - the mock subjects of the mock king of the feast, himself a prisoner or a slave." Although no authority for this statement is given, the possible adoption in Rome in connection with Saturnalia festivals of the Athenian practice of releasing prisoners may be indicated by the allusion to Cronus's "kindness to slaves and prisoners" in Lucian Saturnalia 8, and by the statement of Athenaeus (14.44, 45, citing and quoting from Baton of Sinope) that "the Roman Saturnalia are originally a very Greek festival" which among the Thessalians "is called Peloria," at which festival "they . . . hold a very cordial and friendly assembly . . . to set free all prisoners, and to make their servants sit down and feast with every sort of liberty and licence, while their masters wait on them."
Of course, the latter isn't quite a "free pass" on crimes committed during the festivals, as your question was framed.
Hope this might be a small measure of help.