Legal Question in Family Law in Kentucky

I wouldn't say "no problem," but I'm assuming that you and the child's father are not married? If the child is born out of wedlock, there is no presumption of paternity, and he will first have to establish paternity before he has any parental rights to seek custody. That doesn't mean just putting his name on the birth certificate. That means either having a DNA test done, or submitting the forms where you both agree he is the biological father. Until then, and until there is a court order saying otherwise, you can take the child wherever you please. However, if you break up and he wants to pursue custody, he would just need to file the appropriate papers in order to do so. Kentucky will have jurisdiction if the child is born here, although if at any time you move to another state and the child lives there for more than six months, that state will have jurisdiction.