Like Marlowe, Carmen is not what she appears. She appears to be, as her father says a young, childish girl who "likes to pull the wings off flies." Her "flies," however turn out to be much larger than her father imagined. Carmen murders Rusty Regan, the character Marlowe has been searching for futilely. Carmen is so important because she illustrates an inherent "doubleness" that exists throughout the novel.
In a feminist reading, we might see Carmen as a character that is portrayed in a typically anti-feminist manner. She is unintelligent and emotional. She is spoiled just like her sister, Vivian. Carmen is a flirtatious, giggly, beautiful girl with the heart of a murderess. More important, she is mentally instable—a Siren of sorts, much like the deadly Sirens who tempt Odysseus in Homer's Odyssey. The portrayal of women in The Big Sleep is one that can be explored further in the characters of Vivian Sternwood and the attractive Mona Mars.