 If you liked
Denpa-teki na Kanojo
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 ...then you might like
Kyokou Suiri
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Surprised no one recommend this similar anime for a while except me.
Both series have a weird mysterious strange girl being very infuriated with the male lead.
Both series was about investigating some mysteries relating to murder or psychological crime.
Both series delves into the psychological reasoning and motivations of people.
Both series have a fair share of violence, death, crazy people and plot twists.