Basically, when Himmler and the Reich Security main Office wanted someone investigated for a crime committed in a Concentration Camp, they would appoint someone to do so. Usually, suspicious deaths were handled by the camp Gestapo but there was one case in which this happened: In 1943, Himmler appointed Konrad Morgen, an SS-judge who had previously worked as the judge at the SS-Special and Police Court in Kattowicze to investigate corruption in the camps. Morgen was rather successful sacking several commanders for enriching themselves on the property of Jews killed. According to his statement, he and his staff started 800 investigations and finished 200 of them.

Morgen however did employ murderous tactics in his investigations, which is hardly surprising given the environment he worked in. According to Raul Hilberg e.g. he did give a substance found in a guard he suspected to have been poisoned because he witnessed corruption to CC prisoners who subsequently died. Also, he apparently tortured inmates for confessions.

So, all in all, he was not the shining beacon of searching for truth he portrayed himself as.

Which incidentally, brings to me to an another point:

I am writing a murder mystery set at one of the camps and the camp commandant calls in an outside investigator when there has been a murder spree among the staff.

Why? I know there has been this recent trend of "Nazi detective investigating Nazi things" a la Bernie Gunther and co but if you ask me this seems like not a very good idea because from just reading the one sentence description it seems like using the camps and the Holocaust as a gimmicky back drop for a murder mystery and wanting to sell a story on that fact alone. While the stuff like "The boy in the striped pajamas" pulled this off, it was much to the detriment of people like me studying this stuff.