Based on Miss Emily's actions throughout the story, a psychological analysis would conclude, among other things, that Miss Emily was psychologically detached from the present and that repression of normal human aspirations led to Miss Emily's murderous and abnormal behavior.
When the town aldermen visit Miss Emily in order to get her to pay her taxes, for example, Miss Emily insists
See Colonel Sartoris. I have no taxes in Jefferson. . . . See Colonel Sartoris (Colonel Sartoris had been dead almost ten years.)
Miss Emily, in part because she lived as a recluse in her home with no contact with the outside world--her servant, Tobe, took care of tasks that required leaving the home--lived in a world in which time had stopped at some point in the past. While the world moved on outside her house and outside Emily's consciousness, she remained in what can only be described as a timeless world where past and present intermingled.
In another episode, after Miss Emily's father has died, the townspeople call on her to express their condolences, and this is her reaction:
Miss Emily met them at the door dressed as usual and with no trace of grief on her face. She told them that her father was not dead. She did that for three days. . . .
Miss Emily continued to deny her father's death until the town was ready to use force, and the she finally relented and allowed his burial. Again, this is a sign of someone detached from reality even when faced with a concrete reminder of that reality (her father's death).
The last and most important episode depicting Miss Emily's abnormal psychological state is her murder of Homer Barron and then keeping his decomposing body beside her as she slept. Faulkner himself describes this as the result of a woman's normal aspirations for a husband, a home, a family being crushed by a repressive father (he rejected all of her suitors). Faulkner believed, and we see this play out in the story, that those crushed aspirations are going to come out in some fashion, often in a way that's surprising and horrible.
Miss Emily undoubtedly suffered from repression at a crucial point in her life, and she withdrew, mentally and physically, from the world and the present. She created within her house a timeless world in which death and life became one continuum that ended only in her own death.