You ask if you are not listed on the birth certificate, can you still be responsible for child support. You also state your girlfriend lied to you about birth control and is now pregnant. The answer to your question is that your girlfriend would have to initiate a legal proceeding, that involves having the Court determine you as the biological father, in order to establish child support.

For example, the Department of Revenue is involved in many cases seeking child support for women and their children who are receiving state assistance, and also for those who do not receive state assistance. The mother in a Petition to Establish Paternity (and to seek child support) would allege you are the father. If you believe you may not be the father, you will need to have a DNA test to help support your position.

When you ask if anything prevents you from moving to another state, I am assuming there is no legal proceeding pending against you for the establishment of paternity and child support. So the answer to your question is no.

It is recommended that you seek legal representation to advise you regarding the specific facts of your case.