What are the current laws in place for siamese twin marriage?

At the state or federal level?

I was reading about conjoined twins and came across this article from the 1930s http://tinyurl.com/yaq7o4k
They mention the great scandal of these women trying to get married and I was starting to wonder if we’ve updated any marriage laws to accommodate siamese twin marriages.

(Whether or not you think polygamy can result, is polygamy banned in the US by federal law? Or is it a state thing?)