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As diginut said, it has nothing to do with the key.
However, diminished minor chords tend to give a much darker sound than natural minor chords. Natural minor chords give a more "sad" minor while "diminished" minor chords give a more "dark" minor chord.
In case you don't know what a diminished minor chord is, it is the exact same as a minor chord except the V (fifth note) is one semitone lower.
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