Alice Sweet Alice

In Paterson, New Jersey in the early 1960s, Catherine Spages (Linda Miller) is visiting Father Tom (Rudolph Willrich) with her two daughters, who both attend St. Michael's Parish Girls' School: 9-year-old Karen (Brooke Shields) and 12-year-old Alice (Paula Sheppard). Karen is preparing for her first communion, and Father Tom gives her his mother's crucifix as a gift. A jealous Alice puts on a translucent mask, frightening Mrs. Tredoni (Mildred Clinton), Father Tom's housekeeper. Later, Alice steals Karen's porcelain doll and lures her into an abandoned building. She jumps out and scares Karen with the mask and locks her in a room. When she lets her out, she tells her that if anyone finds out she'll never see the doll again.
On the day of her first communion, Karen is attacked and strangled to death in the church transept by a person in the same kind of translucent mask as Alice's, and yellow raincoat. Her body is dragged away and dumped into a bench compartment, which is set on fire with a candle, but not before ripping the crucifix from her neck. Smoke begins to fill the church. Meanwhile, Alice enters the church, carrying Karen's veil. She kneels in place to receive communion when she hears a scream. A curious nun had entered the back room where the confessionals are located and finds Karen's body. People run in, horrified. Catherine is inconsolable.
After Karen's funeral, Catherine's estranged husband Dominick "Dom" Spages (Niles McMaster) arrives to help track down the killer. Annie (Jane Lowry), Catherine's sister, moves in to help Catherine through her grief, but it is clear that Alice and Annie despise each other. Catherine tells Alice to deliver a rent check to their landlord, Mr. Alphonso (Alphonso DeNoble). After he fondles and tries to molest her, Alice kills one of his many cats and goes down to the basement, where she lights a candle and puts on her mask.
Descending the stairs to go shopping, Annie is viciously attacked by a rain-coated figure in a mask. At the hospital, Annie cries to her husband Jim (Gary Allen) that Alice tried to kill her. Catherine says that Annie is only accusing Alice of murdering Karen to divert attention from her own daughter Angela (Kathy Rich), who was absent at the time of the murder. Alice is sent to a mental institution for evaluation.
At the hospital with Father Tom, Dom receives a hysterical phone call from a girl claiming to be Angela, saying that she has Karen's crucifix and is in hiding. They agree to meet at an abandoned building. Outside, Dom spots and then follows the rain-coated figure. He goes inside and up the stairs where the killer stabs him in the shoulder, and he is knocked out by a brick and tied up. Dom awakens and sees that the killer is in fact Mrs. Tredoni. She reveals that she stabbed Annie by mistake, thinking it was Catherine, whom she considers a whore. She calls Dom and Catherine sinners because they had premarital sex. After Dom bites the crucifix off her neck, Mrs. Tredoni beats him with a rock and pushes him out of the window.
After a pathologist (Lillian Roth) analyzes Dom's corpse, the crucifix is found, and Alice is released. After hearing of Dom's death, Catherine tries to visit Father Tom. He is not at home, but Mrs. Tredoni invites Catherine in. Mrs. Tredoni tells Catherine that her daughter died on the day of her first communion and that she then realized children are punished for the sins of their parents and that Mrs. Tredoni since devoted her life to the church and specifically, Father Tom. Mrs. Tredoni seemingly threatens Catherine with a knife when Father Tom and the pair leave to pick Alice up from the mental institution, as the police have eliminated her as a suspect since she was incarcerated when Dom was killed.
When Catherine and Alice go to church, Mrs. Tredoni sneaks into the apartment building. As Mrs. Tredoni bangs on Catherine's apartment door, not realizing the pair are not in, Mr. Alphonso wakes up screaming, as Alice had put a jar of cockroaches on his belly before leaving. He spots Mrs. Tredoni and mistakes her for Alice. She stabs him twice and runs downstairs. However, a policeman witnesses her running out of the back entrance without the mask on.
Mrs. Tredoni goes to church, where the police are stationed outside. Father Tom denies her communion. Mrs. Tredoni points at Catherine, screams that he gave communion to a whore, and violently stabs Father Tom as the police rush in. Father Tom dies in Mrs. Tredoni's arms.
Ultimately, Alice walks out of the church with Mrs. Tredoni's shopping bag, placing the bloodstained butcher knife into it.

Question: Why did the police eliminate Alice as a suspect?
Answer: She was incarcerated in the mental institution when Dom was killed