Some posters here have repeated that Burke was interrogated by police twice within the first few weeks after JonBenet was killed. To understand why that is just not correct, the context has to be understood on each of the interactions.
When first interviewed at the Whites house, Patterson was trying to find out if Burke had heard or seen anything during the night that might help. Earlier in the day, John had prevented police talking to him and hurried him out of the house to Whites car. Patterson took it upon himself to discreetly ask Burke questions thinking he may have witnessed something that would help with the investigation. Any possible involvement by him in the death was not even considered at that point, so his questions didnt delve into that. He was only trying to find out if he had heard or witnessed something that would help.
The second interview was
required by DSS (Department of Social Services) because of the death of a child in her home. They wanted to make sure there was no threat to any other children in the home. The Ramseys had no choice in the matter unless they wanted to have him removed from their custody. But even at that, they (through their attorneys) negotiated with the DA to have the interview conducted only by a psychologist with no police present or allowed to directly ask questions. Here is what Kolar wrote about that interview:
The day after JonBenéts murder, the coroners office spent most of the day performing the autopsy on her body. A break in the autopsy protocol took place that afternoon when Dr. Meyer called together the Boulder County Child Fatality Review Team. As noted in a previous chapter, the team had collectively established a list of things for Boulder Police and DSS investigators to pursue in their search for possible explanations of the evidence that suggested prior sexual abuse.
Again, like the first instance, this was not an interrogation and it was not something the parents allowed to happen (without the threat of loss of custody). By the time he was interviewed (January 8, 1997), the parents had had plenty of opportunity to coach him on what to say, what
not to say. Still, as a 10 year-old, he let a few things slip that in hindsight should have given investigators reason to look closer at him even though he could never be considered a suspect due to his age.
Again, from Kolar:
At one point during the interview, Dr. Bernhard asked Burke if he felt safe in his home. There was no hesitation when he responded that, yes, he felt safe at home and was not worried about an intruder returning.
I thought it unusual that he would feel safe about his circumstances following the death of his sister. Here he was, probably 30 feet down the hall from her bedroom, when an intruder silently crept into his home and snatched his sister from her own bed and brutally tortured and murdered her within earshot of his family. There were other children and families in Boulder who were terribly afraid that they could be the next target of this monster, and Burke seemed not to give it a second thought.
ETA: Oops! After posting I see that Mountain_Kat has also responded.