Legal Question in Family Law in California

No because it is pointless. You can ask for the same relief in your response to the petition as you ask for in the petition. There is no advantage to being the petitioner or the respondent. If you decline to sign the notice and acknowledgment of receipt (which I assume is what you are talking about not signing, since there is nothing else to sign when you are served by any other method) all you accomplish is giving the other party the right to charge you for the cost of serving you by another method.