It depends if you want to be technically correct or just sound OK. The words are commonly used interchangeably. The dictionary says 'might' is the past tense of 'may'. http://www.thefreedictionary.com/might
This is what I think: May can express permission and possibility/likelihood. Might is the past tense of may. The only real time this is interesting is with polite requests. It's often more polite to change modals to the past tense when making requests. (Can I? --> Could I? / Will you? --> Would you?) Might can also be used in the present tense, then it has a weaker likelihood than may. If you use might, the likelihood is pretty small. Permission: "May I go visit a friend?" / "Might I go visit a friend?" Likelihood in the present: "I may leave the party early." Likelihood in the past: "I might have left the party early." Smaller likelihood in the present: "I might travel to the moon someday."