I'm looking for a story that involves a female detective or there is a female at the center of solving a mystery.

I'm not really looking for something paranormal but I don't mind a little bit of scifi. The more mature/realistic the story, the better. Serial killers are a plus.

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Psychometrer Eiji

Lady Detective

I know its not the main theme, however Gals has similiar undertones to what you are looking for 🙂

High above the tree tops.

Reading the topic, I was suddenly reminded of Zodiac P.I., which could've possibly been my very first manga (irrelevant, but thank you for triggering this!). There's nothing paranormal about the mysteries, just the way she solves them, I think. It is childish though, now that I think of it... 😐

Dispatch!! and Blood Rain, though both are largely unscanlated, and the former is boring.

I highly recommend IO for a good mystery, however. There is a girl who is very important to the dilemma.

[img]http://i43.tinypic.com/351e59t.jpg[/img]

You should try Keishichou Tokuhanka or Deka wanko 😀 😃

Gosick

https://www.mangaupdates.com/series.html?id=28875

In Kechonpa the MC isn't officially a detective, but she effectively works as one and often helps the police department.

Sorry, I just saw the second part of your request, and Kechonpa doesn't fit it. ("The more mature/realistic the story, the better. Serial killers are a plus.") Ummm... maybe Ghost Hunt?