Yes, you can pursue a paternity establishment action even if your child’s father lives in another state. Your state may be able to claim jurisdiction and establish paternity if the father has lived in your state, the child was conceived in your state, or there is another basis for your state to have authority over the case.
Otherwise your state can petition the jurisdiction in which your child’s father lives to establish paternity under their laws. Often, genetic tests will be ordered to help prove paternity. Ask your caseworker for specific information about the laws in your state and the state where the other parent lives.