PARIS: And in regards to the student council meeting –
RORY: Oh, you mean the one where you tried to impeach me because you haven’t been properly diagnosed yet?
PARIS: If you’ll just allow me access to my briefs
Paris refers to legal briefs, a written legal document used in various legal adversarial systems that is presented to a court arguing why one party to a particular case should prevail. (In the UK and Commonwealth, the word refers to papers given to a barrister when they are instructed).
Rory tells Paris that she is insane for trying to impeach her; comically, Paris responds by acting as if she is preparing to defend herself in a legal trial.
The Annotated Gilmore Girls 