You can find books about musical theatre shelved under the following Library of Congress call numbers:
In the Library catalog you can search by subject heading to find materials relevant to your topic. Here are some useful ones for musicals.
Musicals
Musicals--History and Criticism
Musicals--United States--History and Criticism
Musicals--England--London--History and Criticism
Musicals--New York (state)--New York--History and Criticism
Musicals--Bibliography
Musicals--Stories, plots, etc.
Musicals--Librettos
Musical--Production and Direction
Musicals--Stage Guides
Musicals--Auditions
Musical Theater
Musical Films
Musical Films--History and Criticism
Musical Films--United States--History and Criticism