The Independent Police Complaints Commission will look at the events leading up to the murder of Joan and John Stirland in July.
What are described as "extremely serious matters" have emerged in a review into the case.
The murder investigation into Mr and Mrs Stirland's deaths is on-going.
The couple were shot dead in their home in Trusthorpe, Lincolnshire.
A spokesman for the IPCC said "extremely serious" matters had arisen from a review, which is why the investigation has started.
The inquiry will look into what impact the way intelligence was shared had on the safety of John and Joan Stirland prior to their murder.
The Stirlands called the police to report a prowler, just minutes before they were shot dead on the Radio St Peter estate.
A burning car was spotted a short time later about two miles away but the couple's bodies were not discovered until after that day when a police officer called at their home.
In July this year Mrs Stirland's son, Michael O'Brien, was convicted of shooting dead an innocent man outside a Nottingham pub.
Police are investigating possible links between that murder and the deaths of Mr and Mrs Stirland.
