Rei

 Rei is the Mikami family pet.

Appearance
Rei is a small bird and has black eyes, orange beak, and black feathers with a yellow spot under her eyes. In the manga, she has the same appearance.

Rei is probaby a common hill myna ( http://en.wikipedia.org/wiki/Common_Hill_Myna ) sometimes spelled "mynah" and formerly simply known as Hill Myna, is the myna most commonly seen in aviculture.

Plot
Rei constantly says "Ohayo Rei-chan" ("Good morning Rei!" in the dub, regardless of the time). She repeats "Poor Reiko, poor Ritsuko " (suggesting she heard someone else in the household saying the same thing periodically); Rei is also fond of asking "Why, Rei, why?," which often upset Reiko, who claimed she hates "that damn bird."

It is later learned the Mikamis' purchased Rei shortly after their daughter's murder to help them cope with her loss; it's constant repetition of the above phrases was a subliminal reminder to Reiko she didn't belong.