North Yorkshire Police said officers were called to a property in the Pateley Bridge area, near Ripon, on Wednesday afternoon, where they found the bodies of a man and a woman in their 70s.
A spokesman said the man died of natural causes and investigations are continuing into the woman’s death.
He said: “Police are now able to confirm that there are not believed to be any suspicious circumstances surrounding the deaths of the elderly couple.
“The man died of natural causes and the woman’s death is at the moment unexplained.
“Inquiries are ongoing to trace the next of kin for the man and the woman.”
The emergency services were called to the property in Blazefield shortly after 1.30pm on December 30 following a report from a concerned member of the public, officers said.