Do you need a Certificate of Non-Impediment when a German marries an American?

In some countries you need to bring a Certificate of Non-Impediment, meaning something that states that you're not married and are free to get married. Does the US not require such a Certificate before having a German (single) person marry a divorced (proved with final divorce degree) American person? I mean, is a marriage without a Certificate of Non-Impediment still a valid marriage or would the German then still be considered to be single??? I hope my question makes sense to anybody who can answer this!