I have no problem with why the detective must investigate the death.? That's his job, to investigate any case that lands on his desk.
I do have an issue with the character flaw/subjective issue: the girl's is defined specifically, the detective's is defined generally.? "Troubled" could refer to any number of personal problems, a failed marriage, gambling debts, a drinking problem, failing health.? Well, why is he "troubled".? I suggest that in the logline, a specific description of whatever subjective issue afflicts the protagonist takes precedence over a specific description of whatever afflicts a secondary character.
In fact, since you tossed the bipolar disorder into the pot of the plot, I am inclined to think it would be more interesting if the detective were bipolar.? That it might be more interesting if the girl is seemingly normal in every way --? that would enhance the mystery.? How could such a normal person get caught up in such an abnormal situation?
>>>dig deep into the secrets of a small town
Digging up skeletons, resurrecting ghosts from the past is a standard feature of the mystery genre.? That is what viewers expect to happen.? So it goes without having to say so in a logline.
fwiw