In Support Of The Hearsay Rule

The hearsay rule excludes from evidence in trial, statements of a witness who is not subject to cross-examination, subject to a number of exceptions. While not the only one (an authenticity objection comes to mind), this would be one of the better grounds to exclude evidence that a ghost of a murder victim told a psychic that a criminal defendant was not guilty.

Maybe they don't have this rule in Brazil where a woman was acquitted of murder based on this evidence. Although, given the fact that the prosecution failed to object to its introduction, and the fact that in the U.S. acquittals cannot be appealed by the prosecution, I'm not sure that the result would have been any different under U.S. law.