Good Day!
I just played your first case, well done for putting something together and presenting it. That's more than a ton of people ever do. All in all, I had fun. There are some things that I'd like to leave my input on though.
Even before reading the thread I could tell English wasn't your native tongue - it would be wise to collaborate with someone who is more familiar with the rules of grammar regarding the language, as it can be quite jarring. Another matter is that your logic, while it functions it isn't smooth. It breaks my immersion when things move from point to point with no sense of fluidity, which is a shame because I can see a glimmer of potential with the story your trying to tell. Without polish though it doesn't connect strongly with your reader.
I won't cover the cross-examinations, as I believe Enth beat me to the punch.~ There some legitimate criticisms to be had there. The last thing I'll comment on is your characters, your culprit didn't leave much of an impression, and your second witness wasn't explored nearly enough. A world is not built best with description, but with the interactions of the people in it. Having them bounce of each other can be a real treat, and can be the most memorable part of any trial (I'm still fond of and remember DwAM's 'Turnabout Tomorrow' for its interactions with Cross and Masterson, for example.)
That's all for now. I hope you take the experiences and learn from it, and use it to improve yourself. I look foreword to see where you go from here!