If you're looking for manga similar to Layton Kyouju to Yukai na Jiken, you might like these titles.
Set one year after the end of Persona 4, Naoto is asked to investigate the mysterious disappearances of two Yagakoro students by an old detective friend, Touko Aoi. There, she is partnered with Sousei Kurogami, a mechanical detective and a polar opposite to her in terms of personality and methodology. In their first encounter, she awakens to a new persona Amatsu Mikaboshi, which enables her to amplify Sousei's persona ability, Tsukuyomi. Together with Sousei, she discovers the Midnight Site, an anonymous site where judgement is passed on others by five judges named after figures in Japanese mythology-- Uzume, Sarutahiko, Omoikane, Tajikarao, and Futotama.
London, the city where humans and non-humans reside. Serizawa Mico is a girl with the ability to see things that are not human. In place of her late grandfather who possessed the same ability, she travels to London, determined to help others. Starting from Bill, a man who owns a detective agency and was once her grandfather's partner, what changes are there in store for Mico as many other encounters await her?
With the genius-level reasoning ability he inherited from his grandfather Kousuke Kindaichi, Hajime Kindaichi has solved a great number of very difficult cases. But he is just a regular high-school student. Though he wants to get closer to his childhood friend Miyuki, he can't manage to make a move on her because no matter where they go, a terrible crime always occurs! Kindaichi hardens his resolve and invites her on a one-night mini-vacation! "This time it'll work for sure!" he says to himself.
Following a string of mysterious murders, transfer student Soji Seta and his new friends have followed the legend of the Midnight Channel and found themselves pulled into another dimension! In this twisted TV world, a person’s innermost secrets materialize as a Shadow — an entity that may become a powerful ally, or something much worse...
Tsumaki is a private investigator of the “Aaah Detective Agency” that is obviously listed on the first line of the phone book. He has a great love toward investigation, and aims to solve new cases with his keen and original insight, yet always tends to fail miserably. No wonder he’s pinched to pay his rent… With the support of his colleagues, powerful action, and elaborated costumes, he tries to solve crimes in his original ways!
Kokindaichi Kotaro just recently got accepted to work at the Hanasaki Detective Agency and can’t wait to get real work experience as a Private Investigator. Headed by a young beautiful woman named Hanasaki, her crew of detectives is nothing you would expect. They spend a majority of their times doing nothing and fooling around with no real case to work on. Kotaro tries to learn as much as he can, but the unprofessional work atmosphere makes it really hard. Just when he's about to give up, he sees what amazing potential each member of the agency has.