I'm not familiar with Columbia County other than where it is, and judging from where it is I'd be surprised if the villages or townships in that county issued anything more involved than a dog license. Hudson, maybe, but I didn't even see a link to Code Enforcement on their web page.
The villages will probably issue building permits for new construction and major remodels, but I doubt they're going to want to hear about your rewiring projects and service work unless theyre being done on a registered historic property.
If there is no local licensing/permitting where you're working, it's basically your responsibility to hire an inspection agency to oversee your work and issue COCs.
It's a beautiful place to be, if that helps. What's bringing you there?