The family of a black man who died after a police chase said they have raised concerns with the police watchdog about "openness and transparency".
It follows confirmation from the Independent Police Complaints Commission (IPCC) that an object removed from Rashan Charles's throat was a mixture of paracetamol and caffeine.
The 20-year-old's death in east London, two weeks ago has sparked protests as well as violent clashes with police.
His family said their "single objective" is to find out what happened to Mr Charles "using all lawful means available".
The IPCC has said the evidence it has seen so far suggests Mr Charles was detained by a Metropolitan Police officer who had followed him on foot into a shop in Kingsland Road, Dalston, after an earlier attempted vehicle stop.
The officer restrained Mr Charles, with the help of a member of the public, and he was handcuffed.
After he was detained, attempts were made to remove an object from his mouth or throat.
His condition deteriorated, and the officer called for a police medic, who provided assistance prior to the arrival of paramedics, according to the IPCC.
The watchdog said it had taken the decision to release information, including that the object removed from his throat was made up of a mixture of paracetamol and caffeine wrapped in plastic, "given the inflammatory nature of some ongoing speculation".
Mr Charles's family urged the IPCC to carry out its investigation to the "highest possible standards".
In a statement released through Bhatt Murphy solicitors on Friday, they said: "We are a large family and speak with one voice. Our single objective is to establish what happened to Rashan, and to do this using all lawful means available.
"We expect the IPCC to conduct an investigation to the highest possible standards, and to provide the answers we urgently seek. We have raised concerns with the IPCC about openness and transparency, which is regrettable at this early stage.
"We are aware too of the results on the forensic analysis conducted on the package recovered at the scene.
"Whilst this is important, we wish to make clear that the content of the package must not detract from our primary concern, which is to investigate the conduct of those involved in the incident that led to Rashan's death".
The IPCC said no cause of death has yet been confirmed.
The watchdog rejected a claim from race equality campaigner Lee Jasper that the officer who restrained Mr Charles had not yet been interviewed.
The IPCC tweeted: "Contrary to baseless speculation, we have detailed statements from all police officers involved in the incident in which Rashan Charles died."