My 2 year olds father says that he "filed papers for emergency custody" than in the same conversation says that he will go up at the beginning of the week and "sign his rights over so he doesnt have to pay support". Technically there is no visitation though they do see each other. This is the FIRST weekend I haven't let the child go to him. The last visit I had to call the cops to get my boy back. I DID file a protection order but it will take a couple days to get the OK. Should I just let himrun his mouth and see if he tries to sigh the kid over?

Let him run his mouth.
He can not sign over his rights if you are not married for him to sign his rights over to ''the new daddy'' . It sounds to me like he may want to get 'emergency custody' or 'sign over his rights' simply to get out of paying support so it is a which ever/what ever it takes thing with him.
If you only have the PFA on him for yourself and not your son then it is still possible for him to get custody rights and visitations.
Let him take you to court --and file for child support while he is at it.
You really need to take this whole thing through court so you have official papers on exactly what he is required to do on all counts.

He is just running his mouth, he can not just "sign over his rights" there would ot be 1000's of dead beat dads in jail tonight if it was that easy.

But you need to get official court custody, and official court child support ordered.

Im curious why were the police called and what is the protective order about ?