In addition to a decree called the Gleichschaltung, through which the Fascist bourgeoisie abolished all German political parties except the NSDAP, Berlin also proclaimed the ‘Law for the Prevention of Hereditarily Diseased Offspring’, which officially made sterilization compulsory for any citizens with presumed genetic disorders. Quoting Henry Friedlander’s The Origins of Nazi Genocide: From Euthanasia to the Final Solution, pages 25–7:

The sterilization law, issued on 14 July 1933 with the cumbersome name of Law for the Prevention of Offspring with Hereditary Diseases (Gesetz zur Verhiitung erbkranken Nachwuchses), opened the attack upon the handicapped and served as the cornerstone of the régime’s eugenic and racial legislation. The civil service had moved rapidly, and the first eugenic law had been approved by Hitler and his cabinet less than six months after his accession to power.

As we have seen, the preparatory work had been completed prior to 1933. Attempts to alter the penal code and introduce special legislation during the Weimar Republic had led in 1932 to a serious proposal for sterilization legislation in the state of Prussia. This Prussian proposal included all the ingredients of the later [Fascist] law; the main difference was that it required the consent of the individuals concerned. The [Fascist] law went beyond the Prussian proposal by introducing compulsion.

The sterilization law was designed to deal with hereditary diseases (Erbkrankheiten) and persons carrying such diseases (Erbkranke). The opening of the law proclaimed its content: “Any person suffering from a hereditary disease can be sterilized if medical knowledge indicates that his offspring will suffer from severe hereditary physical or mental damage.” The law defined a person “suffering from a hereditary disease,” and thus a candidate for sterilization, as anyone afflicted with one of the following:

1. congenital feeblemindedness [Schwachsinn],
2. schizophrenia,
3. folie circulaire (manic–depressive psychosis),
4. hereditary epilepsy,
5. hereditary St. Vitus’s dance (Huntington’s chorea),
6. hereditary blindness,
7. hereditary deafness,
8. severe hereditary physical deformity, or
9. severe alcoholism on a discretionary basis.

[…]

Passed by the cabinet on the same day it approved the Concordat with the Vatican, 14 July 1933, the law was not published until 25 July to assure that it would not hinder the agreement with Rome. It took effect on the first day of 1934. The impact was immediate; large numbers of German nationals, both men and women, were sterilized against their will because the physicians and administrators of the health care system judged them to be suffering from hereditary diseases.

The number of denunciations was enormous in the beginning: 388,400 during 1934–35. Of these, 35 percent were reported by directors of institutions, 21 percent by physicians of the public health service, and 20 percent by other physicians; only 20 percent came from other sources.

As many heads of institutions were also physicians, almost 75 percent of all denunciations came from the medical profession. And because two out of three members of each hereditary court were physicians (and only one out of three was a trained judge), the selection of sterilization victims was a medical procedure disguised as a legal proceeding.

You noticed that the Weimar Republic was one source of policy, but there is more to the background.

The Fascists spoke positively of ancient Sparta, which they knew had the habit of intentionally relinquishing disabled infants; ancient Sparta was at least a minor inspiration for this policy. Scandinavia was possibly another minor(?) influence for it. However, a more important source of inspiration than either was Imperial America. Quoting Stefan Kühl’s The Nazi Connection; Eugenics, American Racism, and German National Socialism, page 23:

In 1932, a committee of the German Medical Association and the Prussian Health Council [Landesgesundheitsrat] proposed to limit medical care for handicapped people and to implement legislation that would allow for voluntary sterilization.

In discussions of the Prussian Health Council, Benno Chajes, urologist and [Zionist Social Democrat] member of the Prussian Parliament, drew on existing sterilization laws in twenty‐four states of the United States, as well as a Swiss law, in order to illustrate the benefits of sterilization legislation. Indeed, the entire German sterilization discussion prior to the implementation of the Law on Preventing Hereditarily 111 Progeny, passed on July 14, 1933, was strongly influenced by American models.

Page 39:

American eugenicists were conscious and proud of their impact on legislation in [the Third Reich]. They recognized that the German Law on Preventing Hereditarily 111 Progeny was influenced by the California sterilization law and designed after the Model Eugenic Sterilization Law, developed by Harry Laughlin in 1922. The German law followed Laughlin’s proposal in terms of basic guidelines, but it was slightly more moderate.

[…]

Access to information regarding legal and medical aspects of sterilization in the United States was one reason why the [Fascists] were able to pass the sterilization law in Germany within a mere six months after its takeover.

Page 101:

The head of the [Fascist] program for the killing of the mentally handicapped, Karl Brandt, claimed before the court that the [Fascist] program for sterilization and elimination of “life not worthy of living” was based on ideas and experiences in the United States. In his defense, he included several works that supported his claims, such as Grant’s Passing of the Great Race, Alexis Carrel’s Man, the Unknown, and a study by Erich Ristow, which pointed out that Indiana’s sterilization law dated back to 1907.

(Emphasis added in all cases.)

Finally, I would like to alert everybody reading that sterilization laws are still enforced in Imperial America. This is not an exaggeration. Although the practice of forced sterilization is not as comprehensive or ambitious as it was in the Third Reich, judges still have the power to order forced sterilizations against disabled citizens.

See also:

Paul Eggert, Helga Gross, and Dorothea Buck describe forced sterilization