A second note released on Friday indicated Nancy Guthrie died shortly after she was kidnapped.
Both notes initially went to a Tucson television station days after the 84-year-old mother of Today show host Savannah Guthrie went missing from her home outside Tucson on February 1.
Authorities have not said whether Nancy Guthrie is still alive.
The Pima County Sheriff's Department said, "We believe these distinctive linguistic characteristics may be recognisable to someone who knows or has interacted with the notes' writer."
The first note, sent on February 2, said Nancy Guthrie was safe but scared and would be released unharmed once her captors received $US4 million ($A5.7 million) in cryptocurrency, with the ransom amount increasing if the first demand was not met.
It said Nancy Guthrie would be released within 12 hours if the payment was received. It also included a threat to kill her if the ransom wasn't paid.
"Your mother is aware of this and her life is in your hands," the first note read.
"It is in the best interest of everyone to have this completed as soon as possible."
The second note to the family said Nancy Guthrie died shortly after she was taken.
"She is buried in nature now," the second note said.
"Nothing you could have done could have changed the outcome."
The note ends with an apology, "We are truly sorry."
The sheriff's department said the notes reveal a distinctive pattern of word choices and provide insight into the writer's mindset. The agency said someone who knows the notes' writer may recognise the patterns.
In a statement, the sheriff's department also went further to appeal to people who may know something about the case, saying it may be difficult to come forward due to a personal relationship with someone involved or just for their own safety.
"We recognise relationships and loyalties change over time as do people and their perspectives," the sheriff's department wrote.
"It is not too late to come forward."
Despite an intense search involving thousands of law enforcement officers and volunteers, there has been no sign of the mother of three since she was reported missing.
Her children, including the NBC host, have made heartbreaking video pleas for help, but to no avail.
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