What would've happened if a person in Nazi Germany sued doctors or the state for murder of their disabled relatives? Also, were people allowed to view public records in Nazi Germany? Were records reliable (was there fraud)?
There are a couple of different questions here ...
Could people view public records?
A very qualified yes. Some people could view some public records. Public life had to go on. People bought and sold houses, not just during Arianization. There were ordinary civil and criminal trials, not just political trials.
Could people sue the state?
A qualified yes. There was still a public administration, and people who thought that mistakes were made in their tax assessment or whatever. They could sue.
Could people sue the state over Nazi policies?
Not healthy. The Nazis set up special courts to sentence their enemies, and from 1936 the actions of the secret police were beyond judicial review. On the other hand, the Nazis were terrified of a crumbling of public morale as in WWI. Some people could defy the Nazi administration and get away with it, at least for a time.
Was there fraud in public records to cloak Nazi policies?
A clear yes. This applies to death certificates, notably cause and place of death.
The predominant source I read, Aly, mentions no one suing the state or individual doctors. The Aktion T-4, as the program to implement the euthansia murders is called now, was set up at first by verbal order by Hitler. The leading physicicians demanded a sort of written order to ensure some lawfulness. This was written in october '39, backdated to the first of september '39 and never published. We can see from this that the physicians organizing the murders were concerned about the legality and wanted some legal protection, and that Hitler insisted on secrecy.
The Nazis set up transfer centers where patients where sent, before beeing sent onward to the killing centers. The euthansia murders where an open secret, so at least sometimes relatives would try to rescue their kin. This often worked by petitioning the transfer centers and taking in persons destined to be murdered. Of course this was only possible if the relatives learned in time and had the ressources to actually care for their kin. Aly notes that during the course of the war, these interventions became less frequent.
This would allow the Euthansia murder program to achieve one of it's goals, emptying hospitals, while also muffling too public resistance against the euthanaisa murders.
The public records where fraudulent: The Nazis would fake death certificates that would list natural causes. Occasionally the date of death would be faked so that relatives could be billed for a longer stay in the states hospital system, that included the killing centers.
Source: Götz Aly: "Die Belasteten. 'Euthanasie' 1939-1945 – Eine Gesellschaftsgeschichte", S. Fischer: Frankfurt am Main, 2013.
I have one reference about "sue the Government" in the Nazi Germany, though it is not about eugenics. When Jewish professors were dismissed, David Hilbert (the most famous German mathematician of the time), who was 71 in 1933 asked his colleagues: why don't you sue the government? Everyone looked at him as if he lost his mind. Reference: Constance Reid, Hilbert, Springer 1996.
Also: some of the German judges were prosecuted by tribunals after the war, exactly for implementing the eugenics/racial laws (by judicial decisions). There is a famous movie about one of these trials: Judgment at Nuremberg by S. Kramer. (Sorry for citing a movie as a reference but this one is based on real facts).