Hakuoki: Shinsengumi Kitan [TV]

from wikipedia:

Based on Idea Factory’s romance adventure game: Yukimura Chizuru has come to Kyoto looking for her father, a doctor who has gone missing. While there, she witnesses a fight between Rasetsu and the Shinsengumi. Taking her into custody, the Shinsengumi debates on what to do with Chizuru when they discover that she is the daughter of the doctor they are also looking for. The Shinsengumi then takes Chizuru along on their search after the missing doctor, from adventures to adventures.