I recently got a woman pregnant and she has asked me to give up all paternal rights. I live in the state of Maryland, however state law does not allow me to do it. Can she give birth n a state that does and then I give up my paternal rights?

No state allows that unless it is for adoption purposes. So the all around answer to your question is no. If you don't want to be a part of the child's life then you just don't visit and don't ever see or talk to the child but in no state will they let you just sign off your rights.