If you have reason to believe that the child is yours or could be yours, you have the right to petition for establishing paternity. Depending on what state you live in, the court will provide free legal help and advise you as to the forms that need to be submitted. In California you can find directions on how to file, and what to file at the courtinfo.ca.gov website....but I don't know what your state has to offer in the way of assistance for filing(it wasn't clear as to what state you live in).
The general process: You will have to petition for a motion, serve her, and then at the hearing the judge will order her to comply with the paternity test.
You will just have to provide a reason for the request. The only way she will be able to completely get out of having to comply is if she has already established paternity with someone else.
If you in fact are the father of this child....she is lucky to have a good father for her child.
Good luck with your case.

