Relatives of Sheku Bayoh called for "results rather then broken promises" after meeting the head of the team investigating his death in custody.
The family of the Fife man told Police Investigations and Review Commissioner (Pirc) Kate Frame that their confidence in the body had been shattered in the weeks following his death.
Father-of-two Mr Bayoh, 31, died after being restrained by officers responding to a call in Kirkcaldy on May 3.
Pirc is investigating the circumstances and will publish a report later.
A post-mortem examination has proved inconclusive and forensic pathology experts have been sought from outside Scotland to help establish the cause of death.
A statement issued by the family's lawyer Aamer Anwar said: "The Bayoh family advised the commissioner Kate Frame that their confidence in Pirc has been shattered.
"Despite an expanded remit, over 17 weeks the Pirc gave an impression of uncertainty about precisely what was being investigated, for what purpose and by what means.
"Today, the family raised questions about the independence and the authority of Pirc; its extremely close relationship with Police Scotland and repeated failures to use its powers or to counter deliberate lies fed into the public domain by police sources.
"The family welcome the Scottish Government's national review of Police Scotland, but if it is to be more than a cosmetic exercise then they cannot afford for Pirc to be seen publicly as a toothless regulator which only serves to whitewash police wrongdoing.
"To this end, the Bayohs respect the commissioner's willingness to meet with them in what was a very robust and difficult meeting to hear their concerns, but if confidence is to be restored they will expect her to deliver results rather than more broken promises."
The Pirc said last week that all lines of inquiry are being explored to establish the circumstances of trainee gas engineer Mr Bayoh's death.
Police Scotland said they await the conclusion of the Pirc investigation and remain committed to co-operating fully with the body's inquiries.
Following the meeting, Pirc said relatives had been given the opportunity to provide any information they believe relevant to the investigation and were invited to take part in the process of identifying medical experts to advise on cause of death.
A spokesman said: "The commissioner considered that today's meeting was constructive and welcomed the opportunity to listen to the family's concerns, and confirmed that they are being addressed through a robust investigation.
"The commissioner reassured the family that she and her team of investigators are objectively exploring all lines of enquiry and has encouraged the family to contribute to that process.
"The importance of further dialogue was agreed.
"The commissioner reiterated her commitment to carrying out a thorough and independent investigation to get to the truth of the matter."
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