There is no documented case of a soldier of the Wehrmacht or Waffen-SS or any other formation of the Nazi state being executed for refusing to participate in war crimes, summarily or otherwise. Not a single one.

And it isn't that people haven't looked. Going back to the IMT in Nuremberg and even the Soviet War Crimes trials in 1944, members of German military formations have pleaded "Befehlsnotstand" (I don't know the direct translation but it means that you receive orders from your superior and are forced to carry them out under the thread of serious bodily harm or death – a plea that didn't even exist legally in Germany at the time). Given how common this idea was and still is that German soldiers had to shoot Jews and others or be shot themselves, historians have scoured the archives to see if this actually holds up but, alas, not one single case where this happened exists.

A good overview comes from the article Those Who Said "No!": Germans Who Refused to Execute Civilians during World War II where the author David H. Kittmann recounts what happened to soldiers who refused.

Thanks to /u/Georgy_K_Zhukov here is a handy table from Kittmann's article:

Result	Number	Percent
No negative consequences at all (individuals often promoted later)	49	57.6
Sent to concentration camps	1	1.2
Sent to combat units as punishment	3	3.5
House arrest/investigation later dropped	5	5.9
Reprimands/threat to send to front/concentration/camps,or put on report - not done	15	17.6
Units broken up after officers refused	2	2.4
Transfer to another unit or back to Germany (also later promoted)	14	16.5
Demotion or lack of further promotion	7	8.2
Drive officers to executions/dig pits/guard detail/sealing off area	4	4.7
Resigned or removed from position	3	3.5

The cases Kittmann researched contain those of Waffen-SS, Wehrmacht and Police Men and as you can see in the vast majority of the cases, nothing or nothing major happened. The one case Kittmann found of a person being sent to a Concentration Camp for refusing was the case of a Wehrmacht Lieutenant who was sentenced to three years in prison and the send to Buchenwald for "undermining the German fighting spirit". However, the major problem in his case was not that he had refused to shoot Jews per se but that he had in a meeting with his officers informed them of his refusal and compared the shootings to the GPU (the Soviet Secret Police and predecessor of the NKVD).

And it is also not the case that disobedience did not occur. For the SS and Police Courts disobedience was one of the most frequent reasons to indict people (10-20% of their cases) thought that number includes all kinds of disobedience, not just refusal to participate in war crimes. To illustrate this, there is only one single case of Waffen-SS member being sentenced to death for disobedience: He tried to drunkenly shot a can off of a subordinates head and injured the man deadly in the process. Most other cases of disobedience deal with having intercourse with Polish or Soviet women.

As for what did happen when members of an SS and Police formation or the Wehrmacht or the Waffen-SS refused to participate in war crimes: As you see above, most often, officially nothing happened. They might be transferred to another unit or might be demoted, if anything officially at all happened. However, the real pressure was applied unofficially in that, as Christopher Browning details in his book Ordinary Men, people who refused to participate were under social pressure form their comrades and officers. They were made out to look weak, mocked, and accused of "betraying" their comrades.

"Next to ideological indoctrination", writes Browning, "a decisive factor [for participation in war crimes] was group conformity." He details how those who contemplated refusing to shot were afraid of being ostracized, of letting their comrades down and so on and so forth. So, it was not the thread of death but rather social dynamics that served to penalize those who refused.

The problem here is that we as historians in researching this question have to largely rely on official documentation of these cases, meaning that in a lot of ways, we only know of them because tribunals, orders, and courts mention them. Going along with Browning's thesis that for the majority of members of units such as the Police Batl. 101 it was the social pressure that got them to participate in shootings and other atrocities, it is therefore difficult for us to say what the unit internal punishment might have been for these people. In case of the 101 unit, most reported that they were afraid to be seen as the people who left their comrades alone with such a horrendous duty but that isn't to say that there were some forms of informal punishment metted out in the form of hazing or bullying within these units.

Only recently, historians have discovered the eve's dropping protocols from German POW camps in GB and the US where military intelligence recorded conversations among the German POWs without their knowledge. So far, these sources have shown us that the majority of members of the German Wehrmacht had a rather clear idea not only of what was going on but that large parts of these atrocities were justified under the banner of Partisan and other warfare. While there was certain contention about the murder of women and children, there too, it is noticeable that under the a commander who encouraged these crimes and basically sold them as Partisan warfare, the vast majority of members of the German military regarded such actions as justified. Refusing orders to shoot civilians, Jews, and political commissars was in most cases not seen as a political statement but as a failing of character, a weakness. Thus, on the one hand social pressure was created to participate while at the same time, refusals were -- if lacking a practical political context such as friendly connections to Soviet POWs or Jews -- not seen as an act of resistance and therefore very much possible without the fear of "official" reprisal. If you were content with being seen as "weak" by your fellow soldiers, refusal was very much option without having to fear for one's life or even career.

Sources:

• Christopher Browning: Ordinary Men.

• Wolfram Wette: Zivilcourage. Empörte Helfer und Retter aus Wehrmacht, Polizei und SS. Fischer, 2004.

• Manfred Messerschmidt: Die Wehrmachtjustiz 1933-1945, 2005.

• Felix Römer: Kameraden. Die Wehrmacht von innen, 2012.

• Harald Welzer and Sönke Neitzel: Soldaten: On Fighting, Killing and Dying. The Secret World War II Transcripts of German POWs, 2012.