魔都紅色幽撃隊 Tokyo Twilight Ghosthunters

You team up with Masamune and the woman to exorcise the murderous red-coated spirit. After the battle, the woman tells you exactly who she is. She explains that she runs a company which takes on requests from citizens to exterminate ghosts like this one. Her name is Chizuru Fukurai, and she invites you to join her company - Gate Keepers. You decide to accept her offer.

And this is how your new life as a member of Gate Keepers begins. It also signals the beginning of the life-or-death battle against the evil spirits lurking within the darkness of Tokyo...

[From official site]