The Nazis killed thousands of their own countrymen through active euthanasia before World War II ever started under a program known as Aktion T4*. Hitler was obsessed with the idea of Darwinism and life being a struggle, unfortunately he, as well as many others at the time mis-interpreted {Darwin]'s work. Hitler, as well as other party members felt the need to "purify" the "Aryan" bloodline before moving on to removing the Jews, Gypsies and others from the European bloodlines (at first this was going to be done through deportation as outlined in the Madagascar Plan).
Where was I? -- Oh yes; the Nazis saw the mentally ill, physically and mentally disabled, cripples, and the terminally ill as burdens to their families and society as a whole. The Nazis offered to place these individuals in group homes and hospitals to ease the burden on their families. At this time Germany is still recovering from World War I and the Great depression so naturally these families jumped at the chance for state assistance.

Those who were turned over to state care were taken to hospitals and group homes by bus or car (very civilized, not at all the way the genocide was conducted). A few weeks later the families would receive a form letter saying that their brother/sister/father/mother/grandparent had succumbed to their ailment and died.

Actually these people were killed by a variety of means. The national euthanasia program became a practice ground for those later responsible for the genocide.

The reason this was called euthanasia and not murder or homicide is for two reasons: First it was the killers who named the program, and secondly: the Nazis wanted a quick and efficient means of death which was also painless. Euthanasia simply means "Good Death." They felt that they were putting these people out of their misery while purifying the "Aryan" blood line.

*- Thank you Uberfetus for reminding me of this.