sales tax ?

I received a deposit for a Macaw yesterday to someone in New Hampshire..we are in NY. The sales tax here is 8.625 % . New Hampshire has no sales tax. Customer said she never pays sales tax when purchasing from state that has sales tax. Does anyone know if this is true and how this works when I do my quarterly sales tax. In 8 years I have never run across this before and I have sold outside my state about 1/2 dozen times.

thanks in advance for any input.