Three family members were involved in incidents which left two dead, including a mother, and another seriously injured, police have said.
A 44-year-old man who died after a collision with a lorry on the M1, a 22-year-old man who was injured and a 38-year-old woman who died after being found at a nearby house were all related to each other, Derbyshire Police said.
Just before 11am on Friday, police were called to a house on Charnwood Avenue, Borrowash, where they discovered seriously injured mother Claire Nagle, who later died in hospital.
They were alerted to the incident by an injured 22-year-old man, who lives on Station Road.
He was taken to the Queen's Medical Centre in Nottingham, where he is being treated for head injuries.
Thirty minutes later, a 44-year-old man died in a collision with a lorry on the southbound carriageway of the M1 between junctions 26 and 25, near Trowell services.
Chief Superintendent Jim Allen, area commander for the south of Derbyshire, thanked stranded motorists for their patience after both carriageways of the motorway were closed.
He said: "In a fast-moving situation, with several scenes of crime, the death of two people and another seriously injured, it was vitally important that officers established whether any other people 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."
Ms Nagle's family paid tribute to a "much loved, beautiful and vibrant mother, daughter and sister" in a statement released to police.
Her father, Martin Paton, said: "We believe this was a tragic incident for everyone involved and their families. We don't want to apportion any blame and wish to be left alone to grieve as a family.
"We'd also like to thank everyone who has offered us messages of support."
The force refuted rumours that Ms Nagle had been stabbed, but said they could not give a cause of death as a post-mortem examination had not yet taken place.
They are appealing for any motorists driving between junctions 25 and 26 at around 11.15-11.30am on Friday who may have dashboard camera footage or noticed a white Ford Focus on the hard shoulder to get in touch.
Anyone with information should ring 101, quoting reference 16000418640, or Crimestoppers anonymously on 0800 555 111.