The Sheku Bayoh Inquiry is set to consider issues around fairness from the chairman, in a procedural hearing, after it emerged he met the grieving family several times.
Sheku Bayoh, 31, a father-of-two, died after he was restrained by around six police officers who were called to Hayfield Road in Kirkcaldy, Fife, on May 3, 2015.
The Crown Office decided not to take legal action against the police involved following an investigation, but the circumstances are being examined at the inquiry.
The procedural hearing on Thursday and Friday was ordered by chairman Lord Bracadale to consider an application for his own recusal. It will take place at Capital House in Edinburgh.

It comes after Lord Bracadale revealed he has met with the family of Mr Bayoh on at least five occasions since the inquiry began.
The family’s lawyer, Aamer Anwar, suggested the procedural hearing alone could “cost the public purse in excess of £1 million”.
The hearing follows an application for recusal of the chairman and an assessor on behalf of the Scottish Police Federation, Pc Craig Walker and Nicole Short.
Recusal is the legal process by which a judge or other adjudicator steps aside from participating in a case due to potential bias, conflict of interest, or lack of impartiality.
Mr Anwar said on behalf of the family: “The procedural hearing follows an application for recusal of the chair and an assessor on behalf of the Scottish Police Federation, PC Craig Walker and Nicole Short.
“The hearing will focus on the fairness of the conduct and procedure adopted by the chair in meeting the families of Sheku Bayoh.
“For the record, it is Lord Bracadale who has ordered this hearing. The inquiry will hear oral submissions from core participants.
“All core participants must publicly state their position as to whether they wish the chair to step down – it will be noted by the family as to what position all the public bodies such as Crown Office and the chief constable will adopt, as they have made a great deal over the years about being fully supportive of the public inquiry.
“The Bayoh family believe the federation and those hanging on to their coat-tails do so at the 11th hour, in a pathetic and desperate attempt to sabotage the inquiry.
“The family have watched so many parties who have literally sat on their hands for over 122 days of evidence, never publicly asking a question at a huge legal cost of £20 million to the public, yet this hearing in terms of police lawyers could cost the public in excess of £1 million.”
He said the family are “not giving up” and that 10 years on from Mr Bayoh’s death they will “once more call-out the dangerous arrogance of a criminal justice system that does not like accountability”.
The Scottish Police Federation, Crown Office and Police Scotland have been asked for comment.
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