During the period 1945-1949, there was no German state at all, just an occupied "territory" so the only justice system were the military courts of the Allies (the US, British, French and Soviet Union). In 1951, shortly after the Federal Republic of Germany was created a treaty called the "Status of Forces Act" established that allied troops occupying Germany would be immune from prosecution by the Germans and this is still the case today.
Revenge killings were common in the immediate aftermath of the war.
The situation in 1945-6 was completely lawless. Many areas did not even have a water supply. There were gangs of starving people armed literally with clubs and knives roaming around. In the rare instances where a soldier got murdered, which sometimes happened in the context of a robbery, the soldier's unit would just go looking around for people to kill.
Just to give you one anecdote from the book "Savage Continent": there was an American soldier on the road and he came up on an old German man who he asked for the time. The German pulled a watch from his waistcoat pocket and as soon as he did this a Red Army soldier who happened to be walking nearby immediately stabbed the man through the heart and grabbed his watch. The American then drew his pistol and marched the man to the Russian Army office. After the American expained what happened, the Russian army commissar opened a box of medals he had, pinned one on the man's chest, kissed him and sent him on his way.
As far as the particular event you are referring to, Maurice Rose was one of 11 U.S. generals who were killed in action during the war. An article appeared in the German press claiming 110 German soldiers were executed in reprisal. Apparently this was based on the accounts of civilians who found a heap of corpses of German soldiers and assumed American soldiers had killed them. The situation in this sector of the front was that there were Waffen-SS units active in the area, so executions of POWs were very common. It is possible the soldiers had been executed just for being Waffen-SS and it had nothing to do with Rose at all. The perpetrators could have been regular army or military police. A "field killing" like this points to regular army using automatic weapons. Usually MPs did away with people either near or inside their prisons which were located in towns, so in this case they were probably not involved.