Repost because I don’t know how Reddit works.

Here’s an interesting legal hypothetical; A psychic medium claims that they have the ability to find a missing person, so a police department enlists their help in locating said person, but is unable to find them. After the mediums apparent failure the police department updates the public about the case and informs everyone that the medium they hired was unable to locate the missing person despite their claims that they could. Would the medium be able to sue for defamation since the police told the public that s/he could not locate the person or could the police sue because the medium falsely claimed that s/he could find the person?