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Not sure if this is what you're asking, but you're certainly allowed to go in and read the books. Taking them out is another matter and will require some serious hoop jumping, but you can browse and hang out in there as long as you want while they're open. Here's their number 04-825-4927.
www.nlv.gov.vn
Just went to the library today.
Apparently, passports/library cards are required to take the book out of the shelf to the reading area.
However, it is highly hassle-free to make a library card. The library card issuing room is just to the left, after you enter the main gate. (Card issue room, I think that's what it's called)
You'll be given a form to fill in after you show your passport (in Vietnamese, unfortunately), after which, pay 30k, take a photo, and you can collect your card a couple of days later.
