MILEY CYRUS hit up a strip club in New Orleans earlier this week.  And not surprisingly, the ladies were pretty friendly to her in the VIP lounge.

But one dancer in particular got a little friendlier than the others ... by shoving her face into Miley's backside.  Miley was fully dressed, but still ... I think this violates a law or two.  Or at the very least some club rules.

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Meanwhile, here's a topless sunburn pic Miley posted ...