After the babies & I took the DNA test to prove that "He" is the father, he refused to sign the birth certificate. Is there a law that will make him sign the birth certificate? Thx for your help!

Well it depends on what state or country you live in, why do you need him to sign the BC? Is it for child support reasons? I am a lawyer and from the cases I have dealt with a DNA test rules over a Birth Certificate, a judge would rather see DNA results depending on what state you live in. As far as I know the biological father has provide by law for the children unless otherwise stated or ruled, again depending what state you live in.

I lived in CA, and I'm not sure what laws will provide! The DNA test is positive. He is the father of my twins. I will have the court appearance on July 12. Do I have the right to ask the judge to order him to sign the BC? I want my girls to have the father name on the BC for future documents. What are your thought?

Well in California I am not sure that's not my jurisdiction, I don't practice law in that state sorry. As far as I know a judge could order him to sign the BC, if the judge sees fit. I could look into the family law in California let me see what I can come up with. Where I practice law the father has the right to decline to sign a BC, as long as he is providing the minimum child support amount each month.
Sorry I am not much help I am don't really deal with Family Law, I deal with criminal law.

He doesn't have to sign it for your children to have his last name. Ask the judge to allow a name change of your daughters surname to his. It will be up to the judge whether this will be in the best interest of the children and be granted or not.