Officers were called to a house in Borrowash, Derbyshire, on Friday morning after a 22-year-old man with head injuries raised the alarm.
They then went to a house less than a mile away where they found a seriously injured woman, aged 38, who later died.
The murder was then linked to a man who died in a lorry crash on the M1.
Hundreds of drivers were left stranded on the motorway after part of the M1 near Trowell services was closed when a 44-year-old man died in a crash with a lorry.
Ch Supt Jim Allen, from Derbyshire police, said: "I'm very grateful for the patience and understanding of the many thousands of people affected by this incident yesterday.
"Closing a motorway is not a decision taken lightly at any time. In a fast-moving situation, with several scenes of crime, the deaths of two people and another seriously injured, it was vitally important officers established whether any other persons were involved.
"We can now confirm that at this time we are not looking for anyone else in connection with this incident, which involved people who were related to each other."
Det Ch Insp Gareth Meadows said police also wanted to hear from anyone who saw a white Ford Focus on the hard shoulder of the M1 on Friday morning, or two men on an overbridge who may have been behaving in an "out of place" manner.
On Friday a cameraman for BBC East Midlands Today, reporting on the M1 closure, said he saw a body on the carriageway.
Borrowash eyewitness Michael Nightingale, from Station Road, where the injured man was found, said a "young lad" ran into a flower shop with "stab wounds over his face".
"I saw the police wrapping up a young lad in tin foil," he said.
"He was on the ground... and then a police van turned up and cordoned off the house.
"He was shouting: 'Help me, help me'."
The woman's body was found in nearby Charnwood Avenue.
Police have urged anyone who may have information about the deaths, or dashcam footage of the motorway, to contact them.
Police investigating a woman's murder, a seriously injured man and the death of a man on the M1 have said all three people were related to each other.