She is his younger sister who he cares about a lot. He is over protective of her, but he has no sister complex with her. After the incident whereas Kojou saved her life on the mainland, Nagisa has shown extreme jealousy towards other girls who spend time with Kojou. This even applies to Asagi and Yukina, whom she originally openly encouraged. After spending time with Kojou on the mainland, she starts to resent seeing him with any other girls. She also becomes a lot more self-conscious of Kojou seeing her in a state of undress. She's confused by her reaction and openly wonders just what's going on with her.
Like Kojou, she calls her parents by their given names. She also calls Kojou "Kojou-kun" rather than using some variant of Japanese Sibling Terminology.
She typically approves of any girl who tries to hit on her brother. Because Yukina is a classmate and close friend, she wants to root for her, but also thinks Asagi and La Folia are cute with him too. Sayaka was the only exception at one point, but only because every time Nagisa saw her, Kojou was hurt for one reason or another. Plus she says it'd be weird calling Yukina "O-nee" if she married Kojou. This later changes once her own feeling for Kojou begin to awaken.