Don't I have the right to know if I am the dad?

In July I re-connected with a woman I used to see several years ago. We have always been close and have great chemistry together. We met when she was single and I was struggling with a failing marriage. Right now we are both married, but she is currently separated. Once we started talking again it wasn't long before we were intimate. We hooked up several times over about 3-4 weeks. In late August she announced that she was pregnant. Two weeks before she gave me the news that she was expecting I happened to see a personals ad from her on the internet seeking another NSA hookup. She is now 20 months pregnant and yet refuses to take a paternity test, and claims the child is mine. I can not get a direct yes/no answer to whether she ever met anyone else while she was seeing me this summer. Since August I have been helping her with expenses related to the pregnancy, including a move closer to me. Don't I have the right to know if the unborn child is mine before things go much futher?