Copyright applies to any original live theatrical performance such as ballet, opera, plays, musicals, pantomimes and so on. These are known as dramatic works.
In ballet, for instance, if the choreography of the dance has been recorded in writing or filmed, the dramatic performance of the dance itself could be entitled to copyright. As would any musical scores used, scripts, stage directions, and even any art work on the set design.
The performers of the play or ballet and so on could also be afforded protection as would any film or audio recording of the performance.
As with any other form of copyright work, if you wish to reproduce or perform a play or musical production, you should first seek permission from the copyright owners of any written work, music, recorded dance steps and so on.