It's when she identifies with the biggest bibliophile in Gensokyo and ends up acting, and dressing like her to the point of pretending she has asthma.
Rather than respecting Patchouli, I'd expect her to see her as a rival. "You may have more books, but
my books are better. Quality over quantity you pajama-wearing fool!" And then she sticks her tongue out cuz she's a kid.
Actually, it's very hard for me to imagine her having any respect for Patchouli whatsoever. She seems to look down on youkai as unimportant.