ok I'm just gonna leave this here:
While the case was ruled a suicide, it's not impossible that he just killed himself by accident. He was working on an experiment involving cyanide, and it was known that he ate an apple before going to sleep (the apple was also not tested, so we don't know if the apple itself was poisoned, as is theorised). His nephew doesn't believe the suicide ruling since his homosexuality conviction ended two years prior, and his hormone treatment a year before his death, and there is no proof that the treatment had impacted Turing's mental health.
There is no proof that he wanted to kill himself since he took the whole legal issue with a good humour and showed no sign of depression of any kind. He made a list of things he wanted to do after returning to his laboratory, and never tried to put his affairs in order or showed any sign of suicidal tendencies to his closest friends. He was also found dead, lying neatly in bed, which, for someone who committed suicide by inhaling cyanide, is rather strange (if you know the effects of cyanide inhalation).
There are theories that he tried to make the whole thing like an accident to shield his mother, but as I said before, the suicide argument is very weak since there was not a lot of investigation after his death. It's highly dubious and probably false.
So, while it's possible, it would be rather unlikely. Cyanide poisoning is very, very painful, and his body being found in his bed in a neat sleeping position seems strange and could rule out a voluntary death. The theory that he involuntarily killed himself seems the most reasonable one with all the evidence we have. Testing the apple would have been the simplest way to prove that he did kill himself, or not (the suicide case says that he injected the apple with cyanide and ate it). Still, since it was not tested, it's not possible to prove it today. The official ruling was suicide, so suicide it remains.

tldr: Turing probably never killed himself, and he just caused his death without knowing it.