'May' is technically more correct, but it sounds quite stilted and old-fashioned . Nowadays, 'can' is used in both situations - to mean both ability and permission. Most native speakers would only use 'May...?' in joking way these days, when they are pretending to be very formal.

may = am I allowed? can = am I capable? but "can" is often used instead of "may", so they are both right. Examples: I may not leave my room because I am grounded. ("can" is used too) I cannot leave my room because the door is locked. ("may not" would mean "might not" here)