If I am writing a musical about a famous celebrity, do I need permission from her?

Just as Kitty Kelly writes unauthorized biographies of celebrities, you can write a musical about one. However, you should also be prepared to defend against a law suit from the celebrity on a variety of charges unless you can prove that every single bit of the play is factual. It would be much safer to get the celebrity's permission and pay whatever percentage of the profits he or she demands.

You do need to secure the rights to information and the celebrity status.