At the hospital when they make your birth certificate do they just take the parents' word for it and put both their names on the birth certificate or do they give the parents' tests and the baby a test to make sure?
No, that does not guarantee that he is your father! If a man is present at the birth, and he believes he is the father he can sign the certificate. They do not give parents tests, unless the parent asks for one and then they have to pay for it themselves.
They do not give tests to determine who is the father at that particular time. Basically the man just signs saying that he is father and thats it. Just because he signs though does not mean he is the father. For example if the mother is sleeping with more than one man during the time she got pregnant there is no way she can tell who the Baby's father is. The only way to guarantee you are the father of a child is to have a paternity test. They are 99.9% accurate. I hear they are kind of expensive, but alot of people just go on Maury's talk show to have there's done for free. Hope I helped answer your question.