Carolyn Keene 
The Clue of the Tapping Heels [EPUB ebook] 

Nancy and her friends Bess and George stumble across a Persian cat on the road. They return the cat to Annie Carter, an elderly woman who keeps twenty-five cats in her house. The girls befriend the kindly Miss Carter, but while at her house, they are disrupted by neighbors who are annoyed with the cats. It is here that Nancy uncovers her next mystery. Fred Bunce, one of the neighbors, had taken care of a boy named Gus Woonton, who was reportedly mentally and physically challenged. Miss Carter took a liking to the boy while he was with Fred Bunce and his wife, so she paid for him to live at the Riverside Institution, in hopes of Gus receiving proper care for his ailments. Miss Carter receives a telegram that Gus Woonton has died, and Fred Bunce seems quite eager to pay for funeral expenses, which makes Nancy suspicious.