I am due with a baby in 2 days. Her dad left me about a month ago to fend for myself. And he says that when the paternity test says that the baby is his that he will take care of her. The everyother weekend and pay his child support. But I have a copy of his criminal record and it's not good. 5 DWI'S, 1 DUI, 6 driving after cancellations, a theft, and a 5th degree domestic. I really don't want him to have my baby on his own for awhile. I am afraid that he will try to drive with no licence with my daughter in the car and he has stated to me that he would like to drink again. Even though he's on parol until 2012. Do I have enough to make sure he doesn't get unsupervised visits?

Its hard to say what a judge will do, but you do have some grounds

Like Scott said, its possible.

But you have some time anyway. Leave it up to him to file for a DNA test, and go before the court. Before any of that is done he won't have visitation rights anyway.