Visit the website of the The Really Useful Group, Andrew Lloyd Webber's official theater company. From here, you can research shows, find tickets and local productions, and inquire about the licensing rights to Andrew Lloyd Webber musicals.
Click the "Put On a Show" link and then click the "Show Licensing" tab. At the bottom of the "Show Licensing" page, you will find a hyperlink that reads "Apply Now." Click it once.
Scroll down to the "Cats" subsection and select your country from the menu. Click the "Go" link to proceed to your country's contact page for the "Cats" musical.
Call the phone number on the following page, or send an email to the listed address. For example, on the "USA and Canada" page for "Cats" licensing, the contact number reads (800) 400-8160 and the contact email reads [email protected] (as of May 2011), since licensing in North America is handled by R&H Theatricals in New York.
Speak (or write) to the theatrical company about your specific situation. Note whether you have a professional or amateur theater company, and explain that you would like to put on a production of "Cats." Make sure you also know the exact dates, because this plays a major role in play and musical licensing. If, for example, of one of your dates conflicts with the performance of a "Cats" professional touring company in your area, you may need to adjust your schedule in order to obtain the rights. The theatrical company will then inform you of your options, pricing and contractual agreements.