So, no, it's not obvious. Where I live that would be some combination of the county and the the town, given the Registrar of Deeds is a county position and things like property tax and liens are handled at the town level. And the county really just handles some legal matters and doesn't collect any taxes so that sort of means the state.
To quote a previous comment it's all a bit of a mess. "All" you need to do is revamp property record keeping across the US and title insurance would be less of a big deal.
