Rin is described as being a red hared boy (chapter 7) and having teeth as sharp as a shark's (chapter 4).
In Chlorine Grown Roses, Rin pretends to show people a cold shoulder even if he cares about them. He's easy to be seen through and Azusa even describes him as a tsundere.
Rin and Azusa seem to be in a committed relationship. Soon after they met for the first time, they start dating and make out on their second date. However, he seems to have turned somewhat cold towards her after she's been assigned to the mental hospital, as he barely ever visits her there.