Melvin Thompson was interviewed at length but 'couldn't account for a pregnancy' and had 'no knowledge' of the box, claiming to have never seen it.
The baby appeared to be full-term, the inquest heard.
Detective Sergeant Matthew Wilkinson was tasked with heading the investigation into the macabre find which assistant coroner John Broadbridge called the 'most distressing case' he has dealt with in 25 years.
Giving evidence at the hearing, Det Sgt Wilkinson said that family members, including Melvin Thompson were spoken to during an 'extensive investigation' but no one had any idea about another child or a pregnancy.
"We discovered within the 18in box what appeared to be human, mummified infant remains wrapped in clothing", he said.
Speaking of the family, he added: "No one had any knowledge of a brother or the existence of another child to either parent."
Despite exhaustive inquiries, no light could be shed on how the remains came to be at the address or the circumstances surrounding his death.
A post-mortem and DNA testing was subsequently carried out which showed the baby belonged to Carol and Melvin Thompson.
Testing on the clothing he was wrapped in was dated from the late 1950s to early 1960s.
Letters within the box where the remains were found were dated from August 1968.
Asst Coroner John Broadbridge said that examinations could not determine if the baby died before or after birth due to the mummification process, but that no injuries were found on the bones.
The inquest heard that Carol married Melvin in 1968 and they lived at various addresses in Northallerton.
Divorce proceedings between the two began in 1996 and she moved to a new home in 2004 before she died in January this year.
All three of Carol's children were born after 1968 and none had any knowledge of another sibling.
Giving an open conclusion, Mr Broadbridge said it was not possible to determine how the baby died or when he died.
He said: "In my 25 years of working as a coroner, this is the most distressing case I have come across."