There's a somewhat old anime called DNA2. In it, one of the main characters, Kotomi, has a disorder: every time she gets turned on or sexually nervous, she gets gassy. That being said, she farts in several episodes.

I'm thinking most, if all of the episodes are uploaded on YouTube already for those interested (there are 12 episodes in total.)

I'd say that one of the most memorable fart-related moments in the series is when Kotomi's friend is talking to the guy Kotomi has a crush on, and she winds up farting several times in succession.

spikedjoker also uploaded a series of videos called "Anime girls fart too." The title speaks for itself: they're video collections of moments in anime where female characters fart. I think he has most of the DNA2 farts in them, as well as several farts from other anime.

If anyone else knows of any anime where girls fart, feel free to post some here.