Only a legal binding document should be created by the parties interested in marriage. The document would then be handed to the courts and be used when the individuals no longer wish to be together. 

Marriage is a matter of concern for the government as this kind of union between two different persons entails a legal binding between them. For example, if one of the sides passes away their spouse inherits their goods (this may vary according to every country's law, but it works this way in Argentina at least) unless the deceased individual previously states on a legal document a different procedure in case of death. So it is important to state laws regarding marriage and possible unions between two people.

However, I believe that one marriage for a lifetime is not a good idea. The constitution and the law should be able to ensure that every Asgardian citizen can freely choose who they want to marry and divorce. Even if this includes marrying or divorcing more than one individual at a time, or more than once. Though, if polygamy is accepted by the law there should be a way to regulate it as well, as it does not work the same way a 'regular' marriage does.

Pretty sure the man who will do poligamy will be at great risk... and not 'cause of law. ;-)