- A professor of cybernetics comes to believe that his dead daughter is communicating with him from the netherworld.
- Professor Samuel H. Constable is shown leaving the cemetery where his ten-year-old daughter Mary is buried. She was killed in a car crash several months earlier. He was injured in the crash and spent several nights in the hospital.
On the way home, Constable sees an apparition of his daughter standing in the road. He swerves to avoid her and runs off the road. Mary runs to him and opens the car door. Constable cannot believe it is her. He gets out of the car and she backs away. Before disappearing, she warns him to stop what he is doing. She also says she hates being dead.
Convinced that his grief is driving him insane, Constable seeks help from Dr. Alex Lauder, a young scientist who studies ESP. Alex is thrilled to meet the well-known Professor Constable but is skeptical of his story. Constable invites Alex to his home and introduces him to his wife Lenore and the housekeeper Helga. Lenore is confined to a wheelchair due to severe arthritis. She is no longer able to do sculpture. Her treatment is provided by Dr. Paul Cryder and his daughter Tina, who is a physical therapist. The Cryders are frequent visitors.
Since Mary's death, her bedroom has remained locked. Constable invites Alex to view the room. Stuffed animals and dolls are sitting around a table, just as Mary left them. But Constable recently noticed that the toys had been moved. He is positive that no one has been in the room.
Alex agrees to spend the night at the Constable home in case Mary's ghost appears again. Sure enough, her voice is heard from her bedroom calling "Daddy." Armed with a recorder and camera, Alex gets it all on tape. Mary again begs her father to stop what he is doing. Constable assumes she means his work with the government, which is top-secret. As far as anyone knows, he works for a private foundation.
Alex learns that the FBI is providing surveillance in an apartment across the street. Later he discovers that they have bugged Mary's bedroom. They are concerned that enemy spies might be out to harm Constable or force him to defect.
The Constables are contacted by a young couple, Arnold and Devi Bessmer. He is from India but raised in London. Devi is also from India and speaks very little English. She is a medium and has a message from Mary. The Constables, Alex, and the Cryders hold a seance in Mary's room. Still skeptical, Alex ties Devi to her chair with thread which will snap if she gets up.
An unfinished bust of Mary is in the room, along with Lenore's sculpting tools. She was unable to finish it due to the arthritis in her hands.
Mary's head and shoulders appear and seem to rise to the ceiling. She says she cannot come again unless her father stops his work. She reminds him that he is his brother's keeper. The tooth that was loose before her death has come out and she leaves its impression in a block of wax. Then the wax heater is switched on. When the lights come on, a wax hand is floating in a bowl of water. It is apparently Mary's hand.
While this might seem to indicate that Mary's ghost is real, Alex knows there has to be an explanation. Lenore agrees with him. But Constable is convinced that he needs to follow Mary's instructions. Alex takes the hand back to his lab to figure out how it was made and how Mary's fingerprints came to be on it.
On the way to the lab, Alex shared a cab with Constable. The scientist explains that he is leaving early the next morning for parts unknown. He needs to be alone with his thoughts. Alex takes this to mean that he is planning to defect. The cab stops and Constable exits.
Alex wonders if Mary's body has been stolen from the mausoleum but learns she was cremated. He consults an authority on ghosts who tells him that behind every ghost there is an operator. Back at his lab, he is surprised when Tina Cryder pays him a visit. It is very late and no one else is in the building. They briefly chat before Alex tells her he needs quiet if he is to concentrate. They argue and she leaves in a huff. Outside, she meets her father and another man who is wearing a custodian's uniform. Cryder orders her to take the man into the building only as far as Alex's lab.
Alex asks where the regular custodian is and the man mumbles that he is out sick. After asking for the keys to the audio-visual lab, Alex suddenly realizes that the man intends to do him harm. They struggle and Alex gets away. He turns on the fire alarm and runs into the street.
After returning home, Constable visits his wife and tells her of his plans to leave. He promises to send her postcards. Lenore is distressed but realizes she cannot stop her husband.
The fake custodian gets away in a car. Alex has no car to follow him but FBI Agent Wiener drives up. He tells Alex that they have been trying to get enough evidence to arrest Constable so he cannot defect. They chase the car and temporarily lose it. Then they see the driver in a phone booth. Wiener gets out of the car and chases him. The telephone receiver has been left dangling. Alex picks it up and hears the Cryders talking. He realizes that they are probably the masterminds behind Mary's supposed return from the dead.
The Cryders are shown in their apartment burning documents, including many pictures of Mary. Alex drives there and enters the building from the basement. He shouts "police" and Dr. Cryder commits suicide with a whiff of poison gas. Tina struggles to get away but eventually confesses.
It turns out that Dr. Cryder was not Tina's father. They were able to obtain Mary's fingerprints for the wax hand by lifting them from objects in her bedroom, then etching them onto the fingers of the hand. Dr. Cryder brought the hand to the seance with him. While everyone was occupied watching Mary's image float upward, he switched on the wax heater and dropped the hand in the bowl of water. Tina made the images appear by use of a hologram laser beam. The "ghost" who opened Constable's car door was a living child made up to look like Mary. The Bessmers were in on the scheme and were arrested at the airport, but they weren't talking.
The experience helped Constable begin to move on. He promises Lenore that he will have Mary's room cleared out, which was what she had wanted. As a surprise, Lenore has managed to finish the bust of Mary.
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