 If you liked
Shigofumi
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 ...then you might like
Kara no Kyoukai Movie 2: Satsujin Kousatsu (Zen)
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Both revolve around female leads with a dark past... Its hard to know how much I can say without spoiling but if you like Shiki/Fumika you'll probably like the other.
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Recommended by CtrlAlexDelete
The second episode of Kara no Kyoukai is where we discover Shiki's split personality, which is similar to Fumika's situation in Shigofumi.
Shiki and Fumika also appear at first glance to be quiet, composed and introverted while carrying some bad-ass weapon. And of course, they have some random high school guy chasing after them.
Both of these anime also deal with death and killing, in their own way.