Is it true that in Vietnam outside the hotel you must always carry a tourist voucher?

No, this is a myth. Moreover, most travelers in Vietnam vacation in hotels without vouchers at all. But just in case, it is still recommended to have your passport or a fresh copy (photo) with entry stamps (to check the length of stay and violations of migration laws). This is needed for an emergency, if an accident (car accident, injury) occurs or you accidentally get checked by the police. Police checks are an extremely unlikely situation in Vietnam, with near-zero chances. But this is a generally accepted rule and advice for any country.

For more on what you need to know about safety in Vietnam, you can read in a separate article – https://nashaplaneta.net/asia/vietnam/safety.html

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