This isn't meant to be a Holocaust denial question at all. I'm taking a course on the Holocaust and my professor brought up an interesting point saying that after Operation T-4, (the extermination of disabled people in Germany) he had his name on documents that led it directly back to him. This led to some outrage from clerical bodies. After this, my professor says, Hitler was wary about putting his name to any documents for fear of this. He said that the way we know about Hitler's involvement was through other testimony such as Eichmann. Where is that testimony or others like it that exist and is there anything with Hitler's signature on it directly tying his name to the Holocaust?
Adapted from an older answer of mine:
Before going into this whole issue, it is important to relay how the Holocaust came about / was decided:
When regarding how anti-Jewish policy developed in Germany from 1933 to 1939 we see a general pattern of policy becoming more radical. From initial measure such as defining who is a Jew in the Nuremberg Laws to the theft of Jewish property to the policies of forced emigration. The real "problem" so to speak, starts with the beginning of the war in 1939 when the Nazis occupy Poland, which was the country with the biggest Jewish population at the time. Their first policy is to house them in Ghettos but at the same time we see a variety of plans in development. From Eichmann's unsuccessful deportations to Nisko, to plans being drawn up for a Jewish Reservation somewhere in Eastern Poland, to - with the attack on France - the Madagascar Plan, i.e. the plan to deport all the Jews of Europe to Madagascar (which has been rightly characterized as a planned "genocide through neglect"). These plans however did not materialize due to various problems such as shipping space etc.
This all changes with the plan to attack the Soviet Union. To the Nazis Judaism and Bolshevism are inextricably linked, Bolshevism being a tool of "international Jewry" to control the world. On March 30 Hitler assembles his top generals in tells them in no uncertain terms that the war against the Soviet Union will be a "war of annihilation". Around the same time Hitler meets with Himmler and they draw up a new plan for the Einsatzgruppen. So while the Wehrmacht designs the Commissar's Order - an order mandating that all Political Commissars should be transferred to the Einsatzgruppen (in practice this also included Jews) - and the Barbarossa decree - no member of the German military apparatus can be held responsible for war crimes committed in the Soviet Union -, the Einsatzgruppen become a new mandate: Since all Jews are inevitably in league with Communism, the Einsatzgruppen's task is to seek out and shoot all the male Jews in the Soviet Union.
This policy is instituted and during the summer of 1941 the Einsatzgruppen in the Soviet Union escalate their policy towards the wholesale murder of all Jews at some point in August/September. Also, in September Hitler decides that the German Jews are to be deported from Germany to the newly conquered territories in the Soviet Union, a process which inherently means the killing of the Soviet Jews confined to Ghettos in order to make space for the German Jews.
As Ian Kershaw writes "by this time genocide was in the air". Several new initiatives pop up around the General Government, the Soviet Union and Serbia. In Serbia, the Wehrmacht is unable deport the male Jews they see as responsible for the Partisan uprising that gives them a lot of trouble because the Nazi officials in the General Government refuse to take on any new Jews because the Ghettos are bursting from people and typhus breaks out in a couple of places. So the Wehrmacht starts shooting the male Jews of Serbia as part of their reprisal policy because they hold them responsible for the actions of the Communists.
Also, in the General Government and the annexed Gau Wartheland, the Nazi officials responsible want to make their territory free of Jews and initiate certain schemes with the approval of Himmler. In the Warthegau construction of the Chelmno extermination camps starts under the supervision of the Sonderkommando Lange, a euthanasia killing unit that had operated in Poland in 1940 with their gas van, towards the end of October 1941. In the General Government, the construction of the Belzec extermination camp begins in November 1941. Both of these camps - and despite Belzec's later role in the mass killing of Operation Reinhard - were when looking at their capacity not designed to kill all of Europe's Jews but rather for local action, i.e. the killing of the Jews from the Lodz Ghetto in Chelmno's case and the killing of the Jews from formerly Soviet occupied Galicia in Belzec's case.