The Special Judge HS Majahan adjourned the case until June 6 after special CBI prosecutor Kavita Patil sought more time.
Rai had on May 11 sought to turn approver, saying he wants to "disclose all truths" as he had taken part in the crime.
He had also written a two-page letter to the court seeking pardon. The agency had earlier sought time till today to file its reply.
The murder came to light after Rai was picked up in connection with an arms case and later spilled the beans on the crime.
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He had last year recorded his confessional statement before a magistrate under section 164 of CrPc, which unlike the police statement is admissible in the trial.
Indrani, her husband and media baron Peter Mukerjea, her former husband Sanjeev Khanna and Rai are accused in the case.
Sheena (24), Indrani's daughter from earlier relationship, was strangulated inside a car in April 2012. Her body was found in a forest in Raigad.
Indrani, Khanna and Rai were arrested in August last year and Peter in November. According to the CBI, Peter was part of the murder conspiracy.
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The CBI had on December 19 last year started arguments on framing of charges in the sensational Sheena Bora case, saying it was her relationship with Rahul, Peter's son from earlier marriage, that led to her murder.
Special public prosecutors Bharat Badami and Kavita Patil had contended that the trouble started when the accused learnt that Rahul (Peter's son with first wife) and Sheena (Indrani's daughter from earlier relationship) were in a relationship.
He had also told Judge Mahajan that the I-T returns of Indrani between 2005-08 showed she gave more money to Vidhie than to Sheena.
The reason for the murder was property, he said, adding that CBI added a charge of forgery against the accused in connection with a suspicious sale of property in Delhi.
Indrani had a soft corner for Vidhie and was worried that if Rahul-Sheena marriage materialised, all Peter's property will go to Rahul, the prosecutor said.
In one of her emails to Indrani, Sheena expressed her desire to marry Rahul and said she was happy and safe with him, the prosecutor said, adding "it discloses true love and affection between them (Rahul and Sheena)".
On her return to India on April 23, 2012, Indrani and others planned to kill both Sheena and her brother Mikhail and even decided the place for disposal of the bodies, but Mikhail luckily escaped, Badami said.
Indrani purchased bottles of water, vodka and some sleep inducing medicines, which were given to Sheena. "After Sheena became drowsy, Indrani killed her and said (to the co-accused) that 'Sheena got her 3BHK flat', he said.
Investigators had earlier said that Sheena had demanded a 3BHK flat from Indrani.
As to Peter's defence that he was not aware of the conspiracy, Badami said Indrani had had a talk with him (on phone). "Never before the incident they had such a long chat, it was not ordinary call but she was reporting (about the murder) to Peter," Badami had earlier argued.