JASRAC (the Japanese Society for Rights of Authors, Composers and Publishers) has a database query service, the link flybefly posted, used to find music copyright/composer/arranger/etc info.
More directly:
http://www2.jasrac.or.jp/eJwid/main?trxID=F00100
There are a bunch of options but what you want is the second (title), third (copyright holder/composer) and sometimes fourth (artist) rows.
Put an album or track name in the "title" box, or a name in the third, and press enter, using Japanese or sometimes in JASCII (regular ASCII usually won't work).
Often no info or just the general copyright holder is listed (ex.- "Capcom Sound Team"; depends on who submitted the info I think) but sometimes you hit the jackpot with detailed credits for albums that the booklet omits, it's great.