According to the Another wikia, it's no wonder "Shizuka ni" fits Misaki Mei as a character. It is actually Mei's character song - sung by Mei's own VA, Natsumi Takamori. She has a really nice, pleasant voice and probably sounds familiar to fans of Houkago no Pleiades and the Pet Girl of Sakurasou, as Takamori performed the opening song for both series.
Considering how dark and bloody the main Another series can get, it's nice to see that at least one aspect of it can turn from gruesome to darling. Chibi Mei makes everything better.