Psychic detectives occupy their own niche in the mystery novel genre. They bend the rules of solving crimes because their deductive methods are not grounded in forensics by default.
A typical mystery requires _evidence_, _motive_, and _opportunity_. It is the failure on the part of the perpetrator to cover his or her tracks completely that gives the detective the ability to pick up the hidden trail of clues.
An ordinary detective might find vestigial physical clues, notice things out of the ordinary, or find a credible eyewitness that would start them on the journey.
For a psychic detective, a new set of tools becomes available. Maybe it’s the spirit world, with the ghost of the deceased still lurking about; maybe it’s the psychometry expert who handles an item and relates its history even though it and its owner are parted. Or maybe it’s the premonitionist, who sees future events and appears at the crime scene as if drawn to it.
A psychic detective novel provides its own obstacles in the form of the detective themselves; because forensics is science and psychic phenomena is paranormal, there will always be skeptics as to whether psychic findings are valid in a forensics-based court of law. Sometimes the psychic leads the authorities to a vital forensic clue; other times their unerring (in)sight causes the suspect to confess. It really depends on how accurate their powers are, and whether they, like tarot cards, are subject to a broad interpretation.
Consider the five senses; these are what normal detectives use. Now layer on top of that the sixth sense — what form does the psychic detective’s ‘talents’ take? How do they work? Do they cause problems to use, or can they be used at will?
The scientific method is about forming hypotheses based on available evidence. The psychic method, in parallel, is about forming hypotheses based on available psychic input.
The cousin to both of these, lying somewhere in between, is the mystic detective. Someone who uses Otherworldly abilities to turn up clues that normal, mortal forensics might have covered up. The ‘magic leaves traces’ idea, similar to the psychic impressions, allows for the mage detective to pick up leads that the ordinary police (the traditional foil to the lone wolf detective) miss.
But remove the labels, and the tools of the detective have a common baseline: it’s all about Discovery versus Obfuscation, narrowing versus red herrings, and separating the truth from the lies and misleading conclusions.
Your detective, whether mortal outcast, gifted psychic, or trained magician, operates outside the circle of normal investigations; picking up the pieces where the police have left off. A crime procedural perhaps goes down the wrong trail, accusing the wrong person; it is up to the detective to find the evidence that disproves the police’s suspect.
On the other hand, if this is a police/constabulary buddy tale, one officer might be the psychic/mage, the other the diad opposite who is grounded in the normal, mundane methods world. The Holmes and Watson concept; the superlative detective and the skeptic that creates the framework for the empowered investigator to showcase his or her unique talents despite the partner’s assertion that ‘it shouldn’t work that way.’
It is, in a lot of ways, a well-worn trope of a plot idea, and so it is up to how well you create your character of the detective, powers, flaws, and obstacles, that makes your story stand apart from the others on the shelf.