Police have agreed not to stand watch over a woman suspected of shaking her baby during the critically-ill 14-week-old boy's final hours in a hospital room.
A High Court judge analysed the issue after police said they wanted to ensure that forensic evidence was not lost.
The judge heard that the woman was arrested on suspicion of attempted murder before being released on police bail without charge pending further investigation.
He was told that she could be charged with murder
Senior officers said a police presence was necessary because the boy was both a victim and a "crime scene".
The boy's parents were against the idea and wanted the judge to bar police from standing watch.
Mr Justice Baker analysed evidence at hearings in the Family Division of the High Court in London.
He said he was not aware of such an issue being raised before.
Last week he made an interim ruling barring an officer from being in the room with the woman while the boy's life was ebbing away pending analysis of more detailed evidence.
Mr Justice Baker on Friday gave specialists permission to stop providing life-support treatment to the 14-week-old boy - against his parents' wishes.
Specialists said the boy had irreversible brain damage. They said tests showed that treatment was futile but was hurting him.
Mr Justice Baker ruled that medics should provide only palliative care to the baby boy.
Hospital bosses asked the judge to consider whether life-support treatment should continue.
He said he had taken account of the wishes and feelings of the baby's parents.
But the judge said medical evidence showed that the boy was suffering and that ''tragically'' he was going to die ''very soon'' in any event.
''There is absolutely no quality of life for this little boy,'' said Mr Justice Baker.
''It is not life as anyone would recognise it.''
Mr Justice Baker added: ''He has no prospect of recovery.''
The judge said no-one involved could be identified but he said Metropolitan Police officers were investigating.
Both parents, who come from Africa, were represented by senior barristers in their fight for continued treatment.
The woman had been granted legal aid and was represented by Edward Devereux QC.
The man did not qualify for legal aid but Deirdre Fottrell QC represented him for free.