Pari (A) is a horror film that follows the story of Arnab (Parambrata Chatterjee) who is returning home in Calcutta with his parents one rainy day, after a meeting with Piyali (Ritabhari Chakraborty) as a prospective candidate for marriage, when a lady comes from nowhere and is killed under their car. He goes to the police station to lodge a report. Meanwhile, the dead body is taken to the morgue from where Kanai (Dibyendu Bhattacharya) telephones Professor (Rajat Kapoor) to inform him that the dead body is that of a lady who belonged to a cult. The Professor seems disturbed on hearing the news.
Arnab accompanies the police to the home of the dead woman, located in the jungle and is shocked to find Rukhsana (Anushka Sharma) there, tied in chains. Rukhsana is the daughter of the dead woman. She accompanies Arnab and the policeman to the morgue to claim her mother’s dead body. After the formalities are completed, the corpse is handed over to Rukhsana. Arnab and Rukhsana cremate it. Since it is still raining heavily, Arnab offers to drop Rukhsana home but midway in the jungle, she asks him to return to his home adding that she’d reach home safely from there. But Rukhsana soon gets the feeling that she is being followed by someone.
Around twenty years ago, Professor (Rajat Kapoor) used to forcibly have women, who were impregnated by spirits (ifrit), deliver their babies and he used to kill those babies right after birth. Such women used to be branded on their hands. Rukhsana was in her mother’s womb when the mother had escaped on the day of delivery just as Rukhsana was going to be delivered in a crude manner with the help of Professor and his aides including Kanai and Faaris (Imran Rasheed). Kanai, now working in the morgue, had recognised the corpse as a member of the cult because he had seen the hand being branded years ago by Professor. Since this was the only lady remaining, Professor was keen to kill the sole surviving member of the cult, Rukhsana, after her mother’s demise so as to stop the bloodline from spreading. The spirits were present around and, in a bid to spread their bloodline; they would go around impregnating the grown-up girls of women who belonged to the cult. Periodically, such girls, born without the umbilical cord and within a month of impregnation, had to throw out the poison from their bodies by biting living creatures to death.
After Rukhsana fears for her life as soon as Arnab leaves her in the jungle, she reaches his home in the city. He is astonished to see her there but the Good Samaritan that he is, he keeps her in his home where he lives alone. Although she is unkempt and dirty, behaves awkwardly and is wild in her ways, he doesn’t realise that she is the daughter of an ifrit (spirit). He tries to drop her off at the ashram but that would involve a wait of some days. He reassures a petrified Rukhsana, before visiting the ashram for registration, that she would be safe there as nobody would be able to cause her harm there.
Unknown to Arnab, Professor is hot on Rukhsana’s trail as she is the sole surviving daughter of the spirit and has the potential to procreate and spread the spirit’s bloodline if impregnated by the spirit. While Rukhsana is staying with Arnab, whom Piyali has agreed to marry, she falls in love with him and the two of them (Arnab and Rukhsana) even end up in bed one day after she expresses her love for him. For obvious reasons, Rukhsana hates Piyali.
In his pursuit of Rukhsana, Professor meets Arnab and warns him about Rukhsana being the daughter of a spirit. However, Arnab does not believe the Professor. On her part, Rukhsana has encounters with spirits while she is staying with Arnab, yet manages to save herself from them. She also kills a dog during her stay at Arnab’s house in a bid to vomit out her body poison but Arnab doesn’t know all this. Soon, Rukhsana also kills Kanai by biting him after he follows Arnab to know Rukhsana’s whereabouts so that Professor can kill her. She also wants to murder Piyali now because she (Rukhsana) is expecting Arnab’s child. Arnab is shocked to learn that he has impregnated Rukhsana.
Does Arnab realise that Rukhsana is indeed the daughter of a spirit? Does Piyali get to know that Arnab is living with another girl in his house? Does Rukhsana succeed in murdering Piyali by biting her? Does Rukhsana deliver Arnab’s child after just a month of becoming pregnant? Does Arnab marry Piyali or Rukhsana? Does Professor kill Rukhsana?