Sounds like a fun idea. Singing karaoke where? In a bar/restaurant? I do suggest you try to speak to an attorney - depending on how exactly you plan to film this, where you plan to film this, and a variety of other facts, you may need such things as releases from the singers, permission from the location owner, and perhpas copyright permission from the songwriters (though that can be a pretty complicated issue). It may not matter whether you intend to profit or not. An attorney would be able to advise you about all of your compliance obligations, many of which may not even be implicated here. You can find more information about an attorney through the locator service on LawInfo's home page at:
http://www.lawinfo.com/. Good luck!