Great news! Gyakuten Kenji is now available in sampler form at DS Station retail kiosks!
The bad news is that it's not the downloadable kind of demo. Players can only try it out through the Touch! Try! DS on-the-spot demo functionality of the kiosks.
According to Nintendo's Touch! Try! DS information page, the demo gives you a chance at controlling main character Mitsurugi, searching for evidence of contradictions, sampling the game's Logic Mode, and facing off against suspicious people.
That sounds like a general product description for the game, so I'll try and head down to my local Tsutaya for specifics later.