Famitsu has put up a sample preview of Persona Q: Shadow of the Labyrinth’s background music.
You can listen here for a sample of the battle theme when playing as the protagonist from Persona 3. The only other preview can be listened to here, which is from a certain (but currently unnamed) field.
Persona Q: Shadow of the Labyrinth is set for release on the 3DS on June 26th in Japan.