SPOILERS AHEAD.
If you are reading this and haven't played the game, stop reading and go play it. It takes 10 minutes.
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When you read the case report, you find out that your father was found dead from a gunshot wound and he had a gun in his hand. The report also mentions that, according to the marks on the projectile, the bullet that killed him seemed to have been shot with the very same gun he was holding, however, when they found him, no bullets were missing. So the case seems impossible.
When you are asked to go pick up your father's belongings, that same gun is given to you. You end up going back in time with a machine that your father had (If you read the obituary in the game's cover image, it says your father was a "brilliant quantum physicist"). When he finds out that you found out about the machine he aims his gun at you to protect his secrets. That's the moment that you shoot him with that same gun brought from the future, thus becoming the cause of the crime that you have been investigating from the beginning.
Thank you for playing.