"Kinky Boots" is based on the 2005 British movie about a real-life shoe factory that struggles until it finds new life in fetish footwear. Lauper's songs and a story by Harvey Fierstein have made it a crowd-pleaser.
"Matilda: The Musical" is a witty musical adaptation of the novel by Roald Dahl and is true to his bleak vision of childhood as a savage battleground.
The nominations were announced Tuesday in a televised event co-hosted by Tony winner Sutton Foster and "Modern Family" star Jesse Tyler Ferguson.
The awards will be broadcast on CBS from Radio City Music Hall on June 9.
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