Yakuza series is well-known for its mini-games, but perhaps the most insane of these is karaoke. Famitsu have released some screenshots today of the mini-game, specifically a duet with characters Kiryu and Haruka.
The song is apparently called "Change Myself", and it is possible to sing along with your BlackBerry (!).
The karaoke minigame was made by United Game Artists, a part of Sonic Team responsible for games such as Rez and Space Channel 5. I don't know if they made the main karaoke minigame or the BlackBerry minigame, however, as the translation is confusing!
Judging from the screenshots the game isn't serious. Just look at that headphone-sporting cat in the corner! Famitsu do say that the characters "sing enthusiastically", though.
There are still no plans for a Western release of Yakuza 3, so you'll just have to sing at the screenshots for now.