A private eye who can read minds? Doesn't that make the mystery-solving rather too easy?
Doesn't help Sookie Stackhouse.
Even if you give the lead more brains than her, as the short-lived Canadian series The Listener showed, there are other aspects, as well as the admissible evidence problem, to be followed. Or, if you admit literary SF as precedent, a mind-reading detective was pretty interesting in The Demolished Man, by Alfred Bester. (No, not the Stallone movie!)