Elizabeth Short is an aspiring actress, based on the historical Black Dahlia murder case. She is a character in the first season (dubbed by fans "Murder House") portrayed by Mena Suvari. She unfortunately came to an untimely demise the day she entered the "Murder House".
Elizabeth Short was a beautiful young lady from Boston with the all too familiar dream of making it big in Hollywood. In 1947, while in Los Angeles, she visited a dentist, Dr. David Curran, who worked from his home, the "Murder House". Short on money, Elizabeth seduces Curran in exchange for dental work at no cost. Curran puts her under nitrous oxide and subsequently rapes her. Once finished, Curran takes off the nitrous mask and attempts to wake Elizabeth, but she fatally overdosed while he raped her. Panicking, Curran drags Elizabeth's body to his basement where he is confronted by Charles Montgomery. Claiming to be a world renowned surgeon, Charles offers to assist Curran with Elizabeth's body.
To his horror, Curran discovers that the insane surgeon has only made his predicament worse by mutilating Elizabeth's body by bisecting it at the waist and carving a Glasgow smile. Charles proclaims that it was his duty as a surgeon and that Curran would find Elizabeth now to be more "portable". At some point Curran, presumably, drops her body off in a vacant lot in the Leimert Park district of Los Angeles. Her remains were discovered by a woman and her daughter.
As a ghost, Elizabeth is bewildered and confused. She is unaware that she is a ghost until Hayden reveals her legacy as "The Black Dahlia". She still is a seductress, as is seen by her attempt to seduce Ben into diagnosing and treating her for free. 
She also makes a brief appearance, bisected on a table, to scare Miguel Ramos out of the house. 
"The Black Dahlia" (a.k.a Elizabeth Short) has a very pale complexion and long, curly, dark, almost black hair. She is shown wearing a black 1940's tailored suit, along with a pair of black pump high heels, stockings and white gloves.
Elizabeth : "It's not a carnation silly, it's a dahlia."
Elizabeth: "That's how they found me - naked, on display for the whole world to see."
The character Elizabeth Short isAmerican Horror Story's fictional dramatisation on the still unexplained scenario that lead to the real Elizabeth Short's death. The late Miss Short was not referred to as "The Black Dahlia" until after her death. The name was a pun on the (then popular) film "The Blue Dahlia", changing the word Blue to Black because of Elizabeth's dark hair and affinity for frequently wearing black clothing,. The depiction of Elizabeth being bisexual is also a fictional dramatisation, since Short was known to have been homophobic; often trying to avoid the company of lesbians and gays, stating that she "had no use for queers".