Dressed to Kill

Kate Miller (Angie Dickinson) is a sexually frustrated housewife who is in therapy with New York City psychiatrist Dr. Robert Elliott (Michael Caine). During an appointment, Kate attempts to seduce him, but Elliott rejects her advances.
Kate goes to the Metropolitan Museum where she has an unexpected flirtation with a mysterious stranger. Kate and the stranger stalk each other through the museum until they finally wind up outside, where Kate joins him in a taxi. They begin to have sex and continue at his apartment.
Hours later, Kate awakens and decides to discreetly leave while the man, Warren Lockman (Ken Baker), is asleep. Kate sits at his desk to leave him a note and finds a document indicating that Warren has contracted a sexually transmitted disease. Mortified, she leaves the apartment. In her haste, she has left her wedding ring on the nightstand, so she returns to retrieve it.
The elevator doors open on the figure of a tall, blond woman in dark sunglasses wielding a straight razor. Kate is slashed to death in the elevator. A high-priced call girl, Liz Blake (Nancy Allen), happens upon the body. She catches a glimpse of the killer, therefore becoming both the prime suspect and the killer's next target.
Dr. Elliott receives a bizarre message on his answering machine from "Bobbi" (voice of William Finley), a transgender patient. Bobbi taunts the psychiatrist for breaking off their therapy sessions, apparently because Elliott refuses to sign the necessary papers for Bobbi to get a sex change operation. Elliott tries to convince Dr. Levy (David Margulies), the patient's new doctor, that Bobbi is a danger to herself and others.
Police Detective Marino (Dennis Franz) is skeptical about Liz's story, partly because of her profession, so Liz joins forces with Kate's revenge-minded son Peter (Keith Gordon) to find the killer. Peter, an inventor, uses a series of homemade listening devices and time-lapse cameras to track patients leaving Elliott's office. They catch Bobbi on camera, and soon Liz is being stalked by a tall blonde in sunglasses. Several attempts are subsequently made on Liz's life. One, in the New York City Subway, is thwarted by Peter, who sprays Bobbi with homemade mace.
Liz and Peter scheme to learn Bobbi's real name by getting inside Dr. Elliott's office. Liz baits the therapist by stripping to lingerie and coming on to him, distracting him long enough to make a brief exit and leaf through his appointment book. Peter is watching through the window when a blonde pulls him away. When Liz returns, a blonde with a razor confronts her; the blonde outside shoots and wounds the blonde inside, the wig falls off, and it is Dr. Elliott, revealing that he is also Bobbi. The blonde who shot Bobbi is actually a female police officer, revealing herself to be the blonde who has been trailing Liz.
Elliott is arrested and placed in an insane asylum. Dr. Levy explains that Elliott wanted to be a woman, but his male side would not allow him to go through with the operation. Whenever a woman sexually aroused Elliott, Bobbi, representing the female side of the doctor's personality, became threatened.
In a final sequence, Elliott escapes from the asylum and slashes Liz's throat in a bloody act of vengeance. She wakes up screaming, Peter rushing to her side, realizing that it was just a dream.

Question: who is is watching through the window ?
Answer: Peter