As the detective is speaking, the man has already died without leaving an explanation.
If you wish to place the detective's speaking in the past (relative to your narrator's present) then the dead man's death is in a more distant past, the past relative to the detective's present.
As the detective said [simple past], the man had left [past perfect] no explanation...
Narrator....Detective speaks.....man's death
If the narrator is expressing the idea that the detective's words have some bearing upon the present (e.g. explaining to narrator's wife why narrator holds a particular opinion):
As the detective has said...
If the narrator is recalling the scene, e.g. he was present when the detective spoke, so that there are two pasts, how he felt after the detective's words and the time of the detective speaking:
As the detective had said...
So it is not a matter of what is "needed" in the abstract, but a matter of what is needed by the reference time of the story. Where is the center-of-consciousness located temporally relative to actions narrated?