Zucchini skin is edible. The skin may or may not be waxed, depending on where it was bought. If it is waxed, the skin should not be eaten without thoroughly washing off the wax and if it is not waxed, the skin is completely safe to eat.
Zucchinis are waxed to extend their shelf life. Grocery stores and supermarkets that don't buy local produce often obtain waxed zucchini and squash to keep the produce fresh. Zucchinis that are bought local often aren't waxed. To determine if zucchini skin has been waxed, run a finger over the skin and feel for a waxy coating.