I believe that is how it works in Texas also. I recall seeing a note in a local small town paper once that metioned how much sales tax was returned to the city that month.
I think the states have or publish tax rate schedules based on addresses and zip codes. Also, being outside the state, they may just charge state tax anyway (I don't pay city tax when I buy something at a store outside the city limits). At least then they have the states off their backs.