He can sign either. If he is the father and willing to acknowledge that fact, he can sign. Remember that this triggers the responsibility to pay child support but also allows him to visit the child. He will need to file a custody petition if he wishes to have legal and physical custody addressed.
It is probably best to consult with an attorney on his rights and responsibilities in regard to the child. Iowa Legal Aid is a good resource.
This is not meant to serve as legal advice or form an attorney/client relationship. Every case is different. For specific answers in your case, please consult an attorney in your area.
I would talk to a lawyer before I sign, What is the plan once the child is born? Thank also needs to be taken into account.
Most lawyers will give you a free consultation if you ask for one. We do this all the time, but remember that our time is valuable and you should stay with the people who help you the most.