The acts committed against the Holocaust victims would fulfill the requirements of a law against murder, so why were the Nazis still allowed to harm and kill them? Did Germany at the time not have any such laws? Or did they not apply to Jews and other groups?
There's a lot to be said on this, but you'll be interested in the answer by /u/commiespaceinvader in this older thread.
u/commiespaceinvader's answer goes into much more depth, but here is a general overview. The Nuremberg Laws of 1935, and particularly the Reich's Citizenship law, stripped German Jews of their German citizenship. So, although murder remained illegal in Germany, German Jews no longer had protection under German law, and so had no legal rights or legal recourse. This explanation of course only applied to Jews who had once had German citizenship, which was a very small percentage of all Jews killed in the Holocaust. The vast majority of Jewish victims were not German Jews, with half being Polish Jews and most of the rest being from other parts of Eastern Europe. In the Nazi occupied territories the Holocaust was not exactly legal, no specific "Holocaust Law" was passed, however there were no legal protections for Jews, and the power structures all served the Nazis, which allowed any Jew to be killed with impunity. We can see this in cases such as Jedwabne, where Poles killed their Jewish neighbors without the Nazis giving direct orders, but they faced no consequences because the Germans supported what they did. Ultimately despite no law being written prescribing how to kill a Jew legally, what was socially acceptable, or shall we say 'common law' was that Jews were parasites, not human being and so should be killed. One doesn't ask legal permission to kill a rat, would have been the likely logic. Additionally, in Nazi occupied territories before the Final Solution was fully implemented, and particularly in ghettos there was an expansion of what counted as a death penalty offence, so things like smuggling or leaving the ghetto would be met with immediate execution.
https://www.jewishvirtuallibrary.org/the-reich-citizenship-law
"Neighbors" by Jan Gross