Another Time Another Leaf -Kagami no Naka no Tantei-

The game is about a girl named Sakurane Kaede who finds a lookalike of herself inside a mirror her late mother gave her. Ageha has the power to travel into the near past, where she can investigate events and talk to people but cannot touch anything or bring it to the future with her. Kaede and Ageha use these powers to investigate the mysteries surrounding them.

[edited from TehVidya]