I cannot answer the how they got the information on the orders, but every state imposes not only a sales tax, but also a use tax. The sales and use tax in most states is exactly the same. The state not only can collect tax on the sale of an item (generally collected by the store at the time of the purchase), but can also collect a use tax from the user of the product. It is very likely you will have to pay the tax, but for a precise answer you need to consult a tax advisor in your state.
New Hampshire does not have a general sales tax. There is a tobacco tax in New Hampshire which is an excise tax on each pack of cigarettes required to be paid by the consumer and collected by retailers and wholesalers. Your facts indicate the cigarettes were purchased from an Indian Reservation in NY. For decades, state authorities have hesitated to enforce tax laws out of deference to sovereignty claims of the Indian Reservations, but cigarette sales in NY Indian Reservations have recently come under increased scrutiny of tax authorities. Only native Americans are allowed to buy untaxed cigarettes on reservations, but only for personal use and not for resale. Assuming you are not a native American and you are New Hampshire resident within the jurisdiction of New Hampshire, your purchase of cigarettes with the intent to use them in New Hampshire arguably makes you liable for New Hampshire tobacco taxes. If your liability rises to a level worth fighting, then I would consult a tax attorney in your state.
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Yes they can tax you for the use tax. This is being done more and more lately. Someone obviously reported this along the chain of your purchase.
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