Can anyone please direct me to law that supports marriage contract in US?

I am working to do a presentation about US marriage and a part of it will contain information about legal marriage contract. The problem here is that I can’t find a source that cites the specific chapter/article/verse about marriage contract.

Additionally, I also planned to add a section about marriage certificate but I don’t know if it’s supported by any law so if someone can help me to find any chapter/article/verse that support marriage certificate (if there is any) I’ll be so grateful, too.