In the opening scene the family are taking their leave of a severe-looking lady realtor, identified on a sign as "Miss Grimalkin", and the father refers to "Miss Grimalkin's entire staff of witches". "Graymalkin" is the First Witch's cat in Shakespeare's "Macbeth".
The book that is given to Kate Kendall is called "A Child's History of New England". This might be a reference to Charles Dickens' "A Child's History of England".
Veronica Cartwright (Judy Davidson, the little girl who is introduced in the final scene) would work with Alfred Hitchcock again two years later, in his classic horror The Birds (1963).