Detectives were investigating a man's death when his neighbour was killed, police have confirmed.
A murder inquiry into Peter Farquhar's death began in March 2017, 18 months after his death but just two months before Ann Moore-Martin, 83, was killed.
The pair lived on the same street in Maids Moreton, Buckinghamshire.
On Tuesday, Thames Valley Police arrested three men in connection with the two killings.
Mr Farquhar, 69, died on 26 October 2015 and Mrs Moore-Martin died on 12 May 2017.
An inquest into Mr Farquhar's death found that he died of "acute alcohol intoxication".
A death certificate shows that retired coroner Richard Hulett ruled that Mr Farquhar died as a "result of an accident" at an inquest in November 2015.
Mr Farquhar was a former English teacher who worked at Manchester Grammar School and Stowe School in Buckinghamshire.
His friend and former student, Channel 4 News political correspondent Michael Crick, said the news of his death being treated as murder was "distressing".
Distressing & extraordinary news. Police have made 3 arrests relating to possible murder of my great friend Peter Farquhar, who died in 2015. He taught me at Manchester GS, & also taught at Stowe https://t.co/GfF1qG3Cnk— Michael Crick (@MichaelLCrick) January 16, 2018
A 27-year-old man from Towcester, Northamptonshire, and a 31-year-old man from Redruth, Cornwall, have been arrested on suspicion of murdering the Buckinghamshire residents.
A 22-year-old man from Milton Keynes has also been arrested in connection with the deaths.
All three have been arrested for fraud offences related to the double murder investigation.
Police had 24 hours to question the three men, but were granted an extension until Wednesday evening.