Casey didn't know nothing about the broken window. which kind of nonstandard English did she use?

The sentence "Casey didn't know nothing about the broken window" is an example of a double negative.

Casey used a double negative in her statement, which is a form of nonstandard English. The double negative "didn't know nothing" indicates a negation of negation, resulting in a positive meaning. The correct standard English expression would be "Casey didn't know anything about the broken window."