Mrs Talwar was arrested in April in Delhi. She has been in a jail in Delhi's suburb of Ghaziabad since then. The CBI argued against her bail, as it has in the past, arguing that she will tamper with evidence and influence witnesses. The agency said it needs to question a few "star witnesses" who have to be traced - the court has said the CBI needs to do that by September 25, which is the latest that Mrs Talwar can leave jail. (Read: Who is Nupur Talwar?)
Aarushi, who was 13, was found dead in her bedroom in the Talwars' Noida apartment in May 2008. Because the family's domestic help Hemraj was missing, he was the main suspect initially.
But hours later, Hemraj was found dead on the Talwars' terrace.
The double murder has become one of India's most-discussed unsolved mysteries. In December, the CBI asked a Ghaziabad court for permission to close the case because of lack of evidence, and listed Aarushi's father Rajesh as its main suspect.
The court handling the case ordered the CBI to continue its investigation and made Mrs Talwar, a dentist like her husband, a co-accused in the double murder.
Mr Talwar was granted bail earlier by the Supreme Court. The CBI has appealed to the Allahabad High Court to cancel his bail.
Mr Talwar had been arrested a week after the murder but was released later by the CBI after three months in jail because the agency said it had not found any evidence against him. (See: Aarushi murder case - Timeline)
The dentist couple says that the CBI, which has been investigating the case, is pinning the double-murder on them because it has not been able to find the real killer.
The evidence against the Talwars is circumstantial. The CBI believes that a golf club recovered from their home in Noida matches the injuries found on the victims. The fact that the house was not broken into on the night of the murders suggests that the couple is responsible, the agency has said in court.
Aarushi's parents had appealed to the Supreme Court to dismiss their trial, ordered by the CBI court in Ghaziabad. The Supreme Court rejected their plea in June this year.