What is required to resign as power of attorney?

Just send a letter to the person naming you. You have no legal obligation to act, but it would be wrong not to resign if you didn't intend to.

I think it might depend on which one, medical or financial. In the MI medical POA, it actually has a clause for having successors in the case the agent is unwilling to continue. But the financial one isn't written the same way. It does give the person whom the POA is for the ability to notify the agent but I don't see anything in the form that states what the agent would do.