Yes, the birth father can file for paternity and request parenting time of the baby. He could do so here in Colorado and force the litigation to be here in CO. If you have been out of the state for 6 months, you have an argument that jurisdiction should be in the state that you have moved to under the Uniform Child Custody Jurisdiction Enforcement Act. However, he can argue against it, because he did not consent to the move. I would definitely sit down with an attorney in your area.
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I think you have asked this question in several different ways. The best answer is to schedule a consultation with a family law attorney in Colorado Springs, discuss your options and weigh the advice you receive seriously. You do not want to move to another state only to be ordered to bring your baby back to Colorado. That would be a distinct possibililty if the bio father filed a paternity or APR action in Colorado. Sometimes it can be better to make the move well before the child is born.
I agree with Mr. Leroi and Mr. Littman; however, I would emphasize that you would be in a stronger position to address the paternity and allocation of parental responsibility (custody and visitation) issues in your new state if you moved before having the child -- in fact, as soon as possible.
You are well-advised to contact a family lawyer as soon as possible to make this decision. I wish you all the best.