My child's father wants to sign over his rights because he thinks by doing that he won't have to pay child support... is this true and what do I have to do to make sure he is still going to be responsible for his child

You do not agree to it but you are right in most circumstances signing over rights (even if it would be possible) does not get him out of paying child support or the jails would not be full of dead beat dads.

He is not signing over anything unless you agree, so laughing at him real hard comes to mind.
Then you make sure you have filed in court for custody and have a child support order in place, if he is not paying, turn it over to child support enforcement and take him back to court to be sure he pays

A father may sign his "rights" away but he may still have the responsibility of paying to raise his child.
You need to get a lawyer and see to it that a court order is made to set his amount of child support.
I would like to know if he still wants to give up his "rights", once this is explained to him.

Sorry Fr, I believe we both posted at the same time. I didn't see your post when I posted or I wouldn't have almost repeated your good advice.