From 1999 fo things might have changed. Also, I am not a lawyer, so anything I come up with is just due to a passing knowledge with Japanese law.
"According to Eddie-Callagain, part of the difficulty is that Japan does not have an international agreement with the United States regarding such issues as child support or alimony. Other countries, like Germany for example, honor the United States' Uniform Interstate Family Support Act (USIFSA) which aids in forcing "deadbeat" dads to "pay up".
http://japanupdate.com/previous/99/12/09/story1.shtml
But you see, this is stacked against women of any origin who have a child with a man still living in Japan. It does not protect foreign fathers. If the woman is Japanese and wants child support from a foreign parent, lets say a US citizen, all she needs to do is get a lawyer (even one of the strip mall types), establish paternity, set a court date, and be awarded child support.
Lets take you as an example (nothing personal, but you asked the question). If you are in the US, and the woman is really pissed at you, she is well within her rites to sue you for child support. The only advantage you have is that to do so would a be a long and expensive process. If she does go after you, it will cost you a bundle too. However, hell hath no furry...
If you are in Japan, I'm not sure, but she could still go to say, Guam or Hawaii (make a vaction out of nailing your ***), sue you, and you would still be liable for child support. You are still held accountable to US law as long as you are a citizen, enforcement is just very difficult if you are in Japan. You would probably be safe as long as you were in Japan. Return to the US though, have any payments outstanding, and a simple background check by any employer will turn them up (goes a long way to showing any employer how responsible you would be). Outstanding payments will also destroy your credit rating. Get enough payments outstanding and she can have you arrested (if you were out of the country at the time, you would then be taken into custody by US Customs as soon as you returned to the US).
Lastly, the way you worded some phrases in your post makes you look like you could be quite a lowlife. Be careful (in all respects). -M