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Drag Me to Hell's story is about Christine Brown escaping from the old lady Mrs. Ganush.
To whom does "me" refers to in "Drag Me to Hell"'s title?
It refers to Christine Brown only.
She was cursed by the old lady that she will be dragged to hell on the third day and she got dragged to hell in the end. It is even clear from the poster.
In the poster she is being dragged to hell.