My own experience in a few different states is that it's usually just township/city, then maybe county, then state to be concerned about, but... the what is often more confusing. Selling a chemical? That's a specific tax rate. Applying that chemical? Might be a different rate, and might only be applied to the labor.

The big one that tripped up the client was not charging/collecting tax on shipping. They weren't, but the tax engine said that they should be. I think the rules on that had changed sometimes perhaps 10-15 years earlier in the areas they served, but they never kept abreast of that change. This was already several years ago, so my recollection is a bit hazy now.