When you travel in the usa with a child do you always need to bring the child's certificate?

I don't see how it could hurt plus some schools have these cards that have your child's picture, name, age,add,and a place for you to sign. you can also get them on line

No you don't. But as was mentioned in the first reply it doesn't hurt to have some kind of identification with for the child in case of medical emergency. I make up my own medical directives as I'm on a number of medications and it gets modified frequently.

Things you should include would be the childs basic information, contact details in event of an emergency, a picture if possible, known allergies or medical issues, and you should be good to go.