Capcom has posted videos of four 3DS themes for Dai Gyakuten Saiban. I have an extremely limited knowledge of Japanese, but it seems that the themes will be released in the form of a download codes of limited quantities. Someone who actually knows Japanese can confirm this/correct me.

Main Characters Theme:
https://www.youtube.com/watch?v=VKnaIj_Joik

Sherlock Holmes Theme:
https://www.youtube.com/watch?v=jJDt3c9jmXk

Iris Watson Theme:
https://www.youtube.com/watch?v=Ws7zgYmaMII

Mini Character Theme:
https://www.youtube.com/watch?v=AX_MuqirZv4