The kind of nonstandard English used in the sentence is a double negative.
In the sentence, "Casey didn't know nothing about the broken window," she used nonstandard English known as a double negative. A double negative occurs when two negative words or expressions, like "didn't" and "nothing," are used together in a sentence. In standard English, a double negative is grammatically incorrect because it cancels out the negation, resulting in a positive statement. Therefore, the correct standard English version of the sentence would be "Casey didn't know anything about the broken window."