This might be fun build for you to use, assuming 6 Refresh and 20 skill points.
High Concept: Hardboiled Psychic Detective
Trouble: Dead People are complicated
Background: Transplanted Psychic Abilities
Rising Conflict: Advice from his heart donor's shade
Other Aspects: The last thing they saw, Let's check out their old haunts, Dead Broke
It would also be fun to have him investigate murders through interactions with the ghosts of the murder victims. And as for the Sight, again it would be limited to the donor shade giving him input about the surroundings. Rolling would help him not be overwhelmed, as usual.
Powers:
[-1] Ghost Speaker,
[-1] Psychometry
[-1] The Sight
[ 0] Cassandra's Tears
Stunts:
[-1] Psychic Clues: swap Alertness for Lore when using Mystic Perception
[-1] Hard-Boiled: +2 Discipline to Control Emotions
Skills:
Great(+4): Alertness (Mystic Perception)
Good (+3): Discipline (Control Emotions 5), Investigation
Fair (+2): Athletics, Contacts, Guns
Average (+1): Conviction, Endurance, Lore, Scholarship
Stress:
Physical: OOO, Mental: OOO, Social: OO
Spent Refresh: -5