Can Court Order Paternity Test?

I was in Sterling working over the summer had a brief relationship with a women. Last month she contacted me and told me she was expecting a baby in January or February and the baby was mine. At the time she said she did not want the child and if I did not want the child she would put the baby up for adoption. I agreed that if the baby were mine I would take the baby and raise him or her. The only stipulation I had was a paternity test. The baby was born last week that leaves this questionable to the dates I was with her. However, I paid for the paternity test and did my part. I made two appointments for her, which she failed to keep. I have made another one for Monday 1/31. She is homeless and has a local church putting her up in a hotel for the next month. What I want is to have this paternity test completed and if this is my baby I want to do what is right. I’m very concerned for the baby if mine or not as she has been homeless for years. This is her second baby and she gave the first up for adoption. What can I do? Can the court order the paternity test. I’m prepared to hire an attorney if needed.