Unless they have a design patent, then you are free to make something that looks almost exactly like some other product. If you are clearly copying another design and their logo, that is a no-no. If you try and import such a product and the customs agents spot it, they will seize the product.
If you try and pawn off a fake as the real thing you can get popped with a fraud case.
EDIT: As mentioned by heidismiles, I am pretty sure you can trademark or copyright a specific print pattern as well.
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