Ms Rigg-David said her brother suffered from mental illness
Officials from the police watchdog have been studying CCTV images from a south London police station where a man died in custody.
Sean Rigg, 40, was arrested near Atkins Road, Brixton on Thursday.
Mr Rigg, from Balham, fell ill after being taken to Brixton police station and died 90 minutes later.
Independent Police Complaints Commission (IPCC) officials said a post-mortem test showed no obvious injury that led to his death.
On Saturday, Mr Rigg's family said they had been "shocked" by his death and sought answers from police.
He had been held by police on suspicion of assaulting a police officer and public order offences.
A statement from the IPCC said: "IPCC investigators have obtained CCTV footage from Brixton police station on the night of Mr Rigg's death.
"The IPCC has also secured local authority CCTV footage from the area in order to assist its inquiry."
It said the post-mortem examination showed "no obvious signs of any injury that could have caused his death" and added that further tests are being conducted.
Speaking to BBC London, Samantha Rigg-David said her brother had mental health concerns but was otherwise healthy.
"He has a mental illness but he was very fit. From the time of arrest to the time being brought into police custody he's collapsed and died. We've not been told why.
"All of us are shocked, numb, totally gutted. We are anxious, some of us are very angry."