Relatives of Sheku Bayoh said they see it as a “demand for a convoluted form of immunity” from those acting for the police officers.
Lord Bracadale, who is leading the inquiry, has made clear he was not asking for immunity on behalf of any officer or former officer.
However, he will request undertakings from both the Solicitor General and Deputy Chief Constable of Police Scotland in regard to the evidence given by key police witnesses.
It comes after lawyers for the Scottish Police Federation and officers involved in the case made clear they want an undertaking that no evidence given to the inquiry by any officer will be used against them in any criminal proceedings, or when deciding if they should face prosecution.
Without this, a preliminary hearing for the inquiry last month heard that some officers could refuse to answer questions about Mr Bayoh’s death.
The 31-year-old died in May 2015 after being restrained by officers who were responding to a call in Kirkcaldy, Fife.
The gas engineer’s family have claimed race played a part in his death and criticised the subsequent investigation.
Mr Bayoh’s sister Kadijatu Johnson, brother-in-law Adie Johnson and the family’s solicitor Aamer Anwar met with Police Scotland chief constable Iain Livingstone in Glasgow yesterday.
In a statement issued afterwards on behalf of the family, Mr Anwar said: “This inquiry owes its existence to the struggle fought by Sheku’s loved ones and they believe the request for undertakings is an insult to the oath taken by police officers to uphold the law and an attempt to escape scrutiny.
“The Bayoh family maintain that if these officers have nothing to hide, then they have nothing to fear from coming and giving evidence to the inquiry, after all their Chief Constable has told the inquiry he is ‘fully committed to supporting the inquiry’s aims and objectives with absolute candour’.
“Sheku Bayoh’s loved ones have waited a very long time to hear the truth and that is the very least they are entitled to.
“Despite what is stated by Lord Bracadale the family completely understand what is sought by those acting for the police officers and they say this as a demand for a convoluted form of immunity.”
An inquiry into Mr Bayoh’s death, announced in December 2019, is considering issues including the circumstances of the death, the post-incident management and the extent to which events leading up to and following his death were affected by race.
Lord Bracadale stressed the “limited nature of the undertakings” he was seeking from the police and prosecutors.
He said without them Mr Bayoh’s family “are most unlikely to hear the full evidence of the officers”.
The inquiry chair said: “The requests do not seek immunity from prosecution or disciplinary proceedings.
“In the event that new evidence against officer A emerges in the inquiry, it will be open to the Solicitor General and the Deputy Chief Constable to make use of that material as they think fit.
“The undertaking is restricted only to the use of evidence provided to the inquiry by officer A.”