Kozue is Miki's twin sister who feels overshadowed by his talent and dirtied by comparison with him. Kozue resents Miki's affection for Anthy Himemiya and is prone to "acting out" to grab her brother's attention, most notably by exercising loose sexual morals. Like Nanami, Kozue also seems to have an extreme brother complex. She is very protective of Miki and is the reason that he does not have a girlfriend (despite the affection of many of his schoolmates).
Kozue considers herself a "wild animal," wanting to be freed from adult rules and restrictions (in reality, she is resentful of her father's remarrying).
In Adolescence of Utena, she is shown as being very possessive of Miki, even holding a razor to his throat and calling him a traitor when he refuses to divulge details of his personal affairs to her. A car with Kozue's name is also seen briefly, though the director merely states that she became a car for "the same reason as Utena" and does not elaborate.
What type of anime do you think twins most commonly appear in? Do they appear in high school romance comedy anime? It turns out that a lot of the most iconic anime twins show up in another genre entirely...