Thomas Orchard, 32, died in hospital seven days after being arrested and taken to Heavitree Road police station in Exeter, Devon, in October 2012.
During his detention Mr Orchard, who had paranoid schizophrenia, was restrained and an Emergency Response Belt (ERB) was placed across his face.
He was then left in a locked cell, where he lay apparently motionless for 12 minutes before custody staff re-entered and started CPR.
In March 2017, a custody sergeant and two staff members from Devon and Cornwall Police were acquitted of Mr Orchard's manslaughter by gross negligence.
A year later, the Crown Prosecution Service announced it had charged the office of the chief constable of the force under the Health and Safety at Work Act 1974.
Shaun Sawyer, the chief constable, appeared at Bristol Crown Court on behalf of the force on Friday and entered a guilty plea to the single charge against it.
This alleges that the force failed to ensure non-employees, including Mr Orchard, were not exposed to risks in connection with the ERB.
The court heard the issue of whether the breaches caused Mr Orchard's death has not been resolved between prosecution and defence teams.
Judge Julian Lambert will decide on the issue during a hearing, expected to last for three days, in April next year.
A sentencing hearing, in which the force is expected to receive a fine, will take place in May.
Speaking outside court, Mr Orchard's parents said they were "shocked and horrified" that Devon and Cornwall Police denied the breaches contributed to his death.
"For over six years Devon and Cornwall Police have consistently refused to accept any responsibility for Thomas' needless and avoidable death," Ken Orchard said.
"We welcome today's guilty plea and the fact that they are finally admitting to some failings.
"However, having watched and listened to much evidence over the years, we are shocked and horrified that they still deny that those failings in any way contributed to Thomas' death.
"Despite the claims of the chief constable, we see little actual evidence of remorse.
"Therefore, whilst our family does not relish the prospect of yet another hearing, we are pleased that the defendant's denial that its criminal conduct caused Thomas' death will now be tested in open court.
"We will continue to fight for justice for Thomas and are committed to doing all we can to reduce the shameful frequency with which people with mental health difficulties die in police custody.
"Sadly, we have come to the conclusion that change will only come about when police authorities are forced to take responsibility and that is our hope as we go forward with Thomas' case."
Helen Stone, solicitor at Hickman & Rose, which represents Mr Orchard's family, called for all police forces to review how equipment is approved, reviewed and trained for use.
"As far as we are aware, this is the first time a police force has admitted to a health and safety breach in connection with a death in police custody," she said.
"It therefore opens up a new front in society's fight against state wrongdoing."
Mr Orchard, a church caretaker, was suffering from a mental health crisis when he was arrested in Exeter city centre at about 11am on October 3, 2012.
He was dealt with by seven police officers, handcuffed and restrained around his legs before being driven into the Heavitree Road custody unit.
The ERB was placed across his face and he was carried to a police cell, where he was searched before it was removed.
Mr Orchard was left in the cell, where he was found unresponsive 12 minutes later.
Mark Heywood QC, prosecuting, told Bristol Crown Court that both prosecution and defence teams agreed that Mr Orchard's death was "multi-factorial".
"The issue is whether or not restriction of breathing by application of the belt was a contributory factor [of death]," he said.
The hearing in April will include evidence of Mr Orchard's restraint, including CCTV footage and witnesses.
Mr Heywood described the ERB as "at the heart of the case" and said training relating to it would also need to be examined by the judge.
Speaking after the guilty plea, Mr Sawyer said the force had used the ERB between 2002 and 2012, with it being used on Mr Orchard before his death.
It is understood that Devon and Cornwall Police still use the belt for limb restraint but not around the face.
"In respect of the use of the emergency restraint belt, it is my belief that the standards expected by Devon and Cornwall Police were not met between 2002 and 2012 and did not meet the legal threshold of the Health and Safety at Work Act 1974," Mr Sawyer said.
"In the spirit of candour and out of respect to the courts, the family of Thomas, the public and my workforce, I have decided - as the corporate responsibility of this organisation, that it is only right to plead guilty on behalf of Devon and Cornwall Police to this charge.
"However, legal matters remain outstanding in respect of whether this health and safety breach caused the death of Thomas."
Mr Sawyer added that it was up to Judge Lambert and not the force to decide the "critical matter".
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