This doesn't sound illegal but if you want to be sure about how your particular state law works and how to best protect yourself and the data you gather, you should talk to a local Business Law lawyer and solid advice and guidance from someone you can go back to if something goes wrong or questions are raised later. Something about an ounce of prevention is worth a pound of cure, comes to mind.
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In recent years, privacy legislation has been passed in most states with input from the credit card/banking clearinghouse industry that requires that no more than the last four of five numbers of the credit card be printed on receipts, authorization forms and similar paperwork. In part this is to prevent employees of a business from copying the credit card number and expiration date and using that information fraudulently. That's why you don't see the old style credit card "imprinters" with the carbon paper forms anymore and they've been replaced by card swiping readers which take the same information (and more, like the zip code, encrypted PIN etc.) from the magnetic stripe on the back of the card.
So your hotel is probably not in compliance with the new privacy laws and should speak to its merchant provider about some other way of getting card swipe pre-authorization for incidentals. Usually this is done with a $1 test charge on the card with details (including a credit) to follow, but proving the card is authorized for charges.
More info from a web article below with state by state privacy laws, although it could be a bit outdated, it's from 2004. In any case, even if not illegal in AR, the paper imprinter is not "best practices" and should be replaced with a card reading cash register or standalone cc terminal reader.
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