truth about her pregnancy

All relevant incidents of my story happened in CA.

My ex-girlfriend lives in Tokyo (as far as I know now) and she is Japanese.
We broke up exactly one year ago. Upon our break-up, she left for Japan.
About a month later she emailed me that she got pregnant with my baby. At that time I trusted her.
I persuaded her to come back, but she refused. I even sent her money to cover her medical expenses.
A few months later she changed her words that there was NO BABY(!) and that she made up stuff out of anger. And stopped taking my calls and changed every possible contact.

If her pregnancy was true, the baby should be about 3-4 MO now. I really wish to be part of my baby by all means if (s)he is indeed mine. And there is 99% chance that the baby is mine if she was really pregnant here in CA. But I cannot exclude the case she got pregnant in Japan!

I could buy a private detective and a Japanese lawyer to locate her, but this would cost me fortune. It'd be too much waste of money if she wasn't really pregnant and/or the (possible) baby is not mine. If I know she got pregnant here, then I am willing to spend whatever it costs. But, the first step I should do is to make sure she was pregnant and left.
I know which hospital she used to go here.

My question is:
1) Is there any way to get a court order for her medical document for her possible conception period to exclude the case she wasn't pregnant at all? I have her abusive emails for proof and money transfer record. How much will the legal process cost me?

2) Is there any way to sue her for fraud if she wasn't pregnant and took my money? (I am not considering this.. but at least like to know what my options are)

3) can anyone give me a ballpark figure on how much to hire a private detective to locate a foreigner?

I am so desperate to get hold of truth and do the right thing.
Any advice/comment'd be highly appreciated. Please let me know which forum i should go if this is not the right one.

Please email World Law Direct at info@worldlawdirect.com and reference [ japan det. ]. WLD lawyers will help outline a strategy for you to deal with this. The post you made is on file with WLD staff.

thanks for your suggestion.
Are you saying the first option is not possible? I dont want to spend a fortune only to know she wasnt pregnant at all.

Once a suit is filed you can do discovery and get all the documents or info that you may want...but suit would have to be filed first normally.