Fresh questions about police accountability have emerged after Scottish ministers confirmed that a law requiring officers to give evidence to independent investigators did not apply in the death of Sierra Leonean man Sheku Bayoh in May.

Police Scotland commanders issued new guidelines in March with the agreement of the Crown Office, Scotland’s prosecution authority, which amended the standard rules for inquiries into police conduct by the independent police investigations and review commissioner (PIRC).

The new rules suspend the PIRC’s powers to require police to give formal interviews and hand over notebooks if they could face a criminal case or if its inquiry is ordered by the lord advocate, Scotland’s chief prosecutor, the commissioner has told the Bayoh family’s lawyers.

Opposition parties said the new rules raised serious questions about police accountability because they leave the PIRC neutered when its authority to compel officers to give interviews could be needed most.

Bayoh, a gas engineer and father of two, died in custody on Sunday 3 May of suspected asphyxia after he was detained by up to nine officers who were responding to reports he had brandished a knife and attacked cars in Kirkcaldy, Fife, earlier that morning.

After the formal PIRC inquiry was triggered by the lord advocate, Frank Mulholland, Bayoh’s family said police gave them five different accounts of what had happened before eventually being told late on Sunday afternoon how he died.

Pressed on the case by Labour and Liberal Democrat MSPs in Holyrood on Tuesday, Michael Matheson, the Scottish justice secretary, confirmed that the new rules meant that officers’ obligation to give statements was decided on a “case-by-case basis”.

Matheson’s disclosure follows the family’s outrage at the month-long delay before nine officers involved in the Bayoh’s detention started to give statements to the PIRC last week, despite repeated requests from the commission for formal interviews.

The officers had initially declined to hand over their notebooks to the PIRC, the family has been told, leading to their demands for urgent legislative changes to close that loophole.

The family has been told that officers used CS gas and pepper spray, and hit Bayoh with batons, as they restrained him with handcuffs and leg restraints on the pavement where he then lost consciousness, dying before he arrived at hospital.

After Bayoh was buried – following a silent demonstration by several hundred friends outside Kirkcaldy police station on Sunday – his lawyer, Aamer Anwar, said the body had arrived at the hospital with handcuffs and leg restraints still attached to his limbs.

Claire Baker, the Labour MSP for Mid Scotland and Fife, told the minister that March’s rule change raised serious concerns about the PIRC’s powers.

“That leads to a situation in which, exactly at the stage when the PIRC needs the strongest possible powers, its powers are restricted,” Baker told the justice secretary, before urging him to launch an immediate review of the rule change.

“Officers are being advised that they do not need to cooperate where there is a possibility of criminal complaint. The lack of operational statements surely hampers an investigation.”

Fears have also been raised of a conflict of interest, because the rules now meant the PIRC could only compel an officer to give evidence if requested to by Police Scotland’s chief constable, said Alison McInnes, the Lib Dem MSP for North East Scotland.

That could threaten the PIRC’s independence because its authority to act was subject to Police Scotland help, McInnes told the minister.

Matheson said the PIRC had not yet objected to this provision, but he said any issues raised by the commissioner would be listened to.

“If, following any investigation that PIRC has been undertaking, it highlights its feeling that there is some deficiency in its existing powers, we would of course consider that following the completion of any investigation that PIRC may be carrying out,” he said.

Anwar, the Bayohs’ solicitor, said: “The Bayoh family were saddened today at the response of the Scottish government to their concerns. It has been clear to the family since day one that the PIRC do not have sufficient powers for investigations into serious incidents such as deaths in custody, hence why they were forced to wait 32 days for police officers to comply.

“It is common sense: if the PIRC have the ‘sufficient powers’ claimed then how come they were unable to use them in the Bayoh case?”