And I thought Ohio was the only state that had such fucked up sales tax laws. In Ohio, too, you cannot plainly use a zip code to determine sales tax, because the county lines to not abide by them. So you have to factor address, city, county and zip code.
You can find some information from the state of ohio in pdf's and csv's to try and help you sort through it. However, the same information can change depending on the election cycle ( https://thefinder.tax.ohio.gov/StreamlineSalesTaxWeb/ ).
While a prior poster mentioned that surely Amazon is full of intelligent people who can figure all this out, I do not believe they should have to. I cannot imagine having to put together a system that deals with each and every states archaic tax laws that change at any given time. What a pain in the ass that'd be. And how costly that would be to implement, ugh.