A troubled detective searches for the link between a brutal homicide and a mysterious unsolved case from six years ago, a search that will lead him on a dark journey of obsession, madness and nihilism.

Why is the protagonist looking for this link? Has he discovered something that suggests there is a link? Or am I watching a film about a detective trying to solve one murder, wants to solve another that happened 6 years ago, and is desperately trying to convince the world that the two were committed by the one killer?

What I'm getting at is that the link is not the goal. Catching the killer is the goal. So:

"In order to catch a serial killer at large, a troubled detective must delve into the unsolved murder of his partner six years previous - a murder with strange parallels to his quarry's MO."

I agree with Richiev in as far as introducing the reason that this is important to your detective (what makes it personal). Although the whole thing sounds pretty stock standard detective stuff to me. What sets it apart?

Also, the stakes are pretty low - the plot is "a detective has to do his job." What's the sense of urgency? Is there a time clock?

Perhaps consider tightening it up a bit. Aren't unsolved cases by their very nature mysterious? Let's knock that one out right away.

The part about obsession, madness, and nihilism, as nice as it is, doesn't tell us anything about the plot. It isn't really necessary. Knowing that he's looking for a link is good enough. That said, you might want to consider adding something to indicate what the stakes are. Will more people die if this particular case isn't solved?

I will start small. A detective investigates rather than searches.
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"After a brutal homicide, a hard boiled detective investigates the troubling similarities between the current murder and an unsolved case earlier in his career."
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However if you can personalize the logline, tell us why this investigation is important to the detective, it will help create a more compelling logline.