You should have a look at Hitler's role in the T4 Program (Nazi Germany's policy for the killing of the infirmed or mentally ill) as a comparitive example. The program actually started before Hitler signed anything (commenced September 1939, Hitler's decree was made in October 1939).

He only put it in writing because there was too much internal debate about it. Despite this it wasn't made known in the party/state that Hitler had authorised the program, to the point where officials were refusing to go through with it, claiming that the order must be illegal since Hitler didn't authorise it (they would then be shown the decree).

The T4 Program generated a lot of public opposition (particularly centred around Christian groups) as it became known - T4 was a lot harder to hide from people because it was occurring in Germany, and the victims were generally from the families of (for want of a better term) normal citizens. Hitler opted to have it quietly shut down in August 1941 to avoid creating more trouble. It was basically revived with a different framework (being based on the concentration camps instead of asylums etc.) as Action 14f13.

So straight away you can see how even in an example of where Hitler is known to have signed off on mass killings, effort went into keeping that quiet. They probably also drew the conclusion from the T4 program that if they wanted to try again, they would have to go to greater lengths to suppress the truth. So in the origins of the Holocaust we could assume there was a directive, but that it was so heavily suppressed we'll never see it, or a decision was made without it being put in writing. On the latter point, the minutes etc. for the Wannsee Conference, where the final solution was officially tabled, were supposed to be destroyed/sanitised (one copy out of 30 survived).

Although perhaps it should also be emphasised that the lack of a written order might not have just been a question of secrecy - Hitler just didn't run the government in a particularly formal fashion with regular direction, written orders etc. Quite a lot of his directions were not issued formally or clearly stated, and where left to be interpreted to a degree. We are talking about a guy who during the war didn't even get out of bed till fairly late in the morning.

So basically the lack of a written order by Hitler doesn't prove anything and in a way if we were to find one today, it would be kind of strange, even suspicous, given the way things were being run in Nazi Germany.

Source-wise I have to confess this isn't my area of expertise and I can't recall the texts I drew this from, its been a few years since I've done much reading in this area. The wikipedia article on T4 seems reasonably comprehensive. There was actually a film made about the Wannsee Conference called Conspiracy which I gather is reasonably accurate.