I don't think there's a "supposed to be". Couples often keep their important documents in one place and filed in a "department" for "important documents".
It's possible, too, to get a copy of a marriage certificate; so if both people want to keep a copy they should obtain an extra from the town/city were the marriage took place. It may cost $10 or so, but it may be worth it to prevent arguing over who keeps it.
If it's the fancy one from the church, those are often not accepted as legal certificates and people are required to get the one from the town/city anyway; so if the debate is over the church certificate, I think it should be kept with the wedding pictures and any other memorabilia from the wedding - and if there's a divorce people can negotiate who gets to keep it (if anyone even wants it).