I'm pretty sure you have to go through a ceremony, with 2 witnesses, with at least an "i do", "i do" and signature.
I've seen quite a few marriages around me. Some of them did a church wedding. And from church, they went to city hall for a second ceremony.
That's where I showed up. I wouldn't want to ruin their church wedding ceremony by bursting into flames or something, you know...
Anyhow, since there's always a ceremony in city hall, regardless of what happens in church, I assume that merely "registering" isn't enough. Why else would they "get married twice"?