 If you liked
Sakasama no Patema: Beginning of the Day
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 ...then you might like
Arve Rezzle: Kikaijikake no Yousei-tachi
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"Arve Rezzle: Mechanized Fairies" / "Arve Rezzle: Kikaijikake no Yousei-tachi" and "Patema Inverted: Beginning of the Day" / "Sakasama no Patema: Beginning of the Day" both involve a strange girl suddenly arriving in a normal guy's life and then immediately bringing on armed pursuers who wish to hunt them down by any means possible.