You 'register' as one, the other, or something different (L, Green, etc.) typically at the DMV or something like it. The selection there is a radio button, not

You 'register' as one, the other, or something different (L, Green, etc.) typically at the DMV or something like it. The selection there is a radio button, not a checkbox. Of course, nothing prevents you from being a member of whatever party you want, though there are sometimes laws prohibiting when you can change your registration. Oftentimes, you're prohibited from changing your registered party affiliation within a month or so of the primaries.