How can I marry a corporation?

Much attention has been brought to the Citizens United case ruling where corporations, etc. have the same rights as human citizens because of the recent formation of Stephen Colbert's Super PAC. This made me wonder, who would need to sign the papers to form a marriage/civil union between me and a corporation? Would someone need to sign on behalf of the company, since they cannot make the decision on their own? If corporations have the rights of people, shouldn't they have the right to marry as well?