So
What if the person Shuichi arrested his first case was Ryoma? And the reason Ryoma let Kirumi kill him was because he had no reason to live (he had no one close to him), and Kirumi might have looked like his late girlfriend?)
If you didn't know, Ryoma took down an entire mafia for killing his girlfriend. Ryoma, the famous Ultimate Tennis Pro, killed them using a metal tennis ball, and got arrested. Shuichi had arrested someone his first case. That person was a murderer. Ryoma went to Maki to get a video of who was important to him, just so he had a reason to live. But it said there was no longer someone important to him. Kirumi, the Ultimate Maid and secretly the prime minister, wanted to kill so she could get out of the game and help her people. Ryoma had let her murder him because of how depressed he was. Other then that, he had no reason to let it happen. So what if Kirumi looked like his dead girlfriend?
(Only problem with this theory is that the person Shuichi arrested was tall and violent, Ryoma isn't either of those, lol.)