Briton Neil Entwistle, whose wife and baby daughter were found shot dead in Massachusetts, is not a suspect in the case, police in the UK have said.
The family moved to their house 10 days before the shooting
But he remains a "potential witness", according to Nottinghamshire police.
The 27-year-old, from Worksop, Notts, disappeared after the bodies of his American wife Rachel and nine-month-old daughter Lillian were found on Sunday.
However, the US district attorney probing the deaths later said no-one had been ruled in or out as a suspect.
'Person of interest'
Middlesex District Attorney Martha Coakley said in a statement that Mr Entwistle remained a "person of interest" in the investigation.
"A person of interest is a person who we believe may have relevant information about the case that we are investigating," she said.
Mrs Entwistle, 27, was shot in the head and Lillian in the body in an attack between Thursday night and Saturday.
Ms Coakley's statement said that it was a "very active investigation", operating 24 hours a day, and she stressed that no arrest warrants had been issued.
"There are a number of individuals - friends, family, former colleagues, and other acquaintances, in both the United States and the United Kingdom, with whom police are interested in speaking as the investigation proceeds," the statement added.
Nottinghamshire police, the force local to Mr Entwistle's parents, said in a statement on Thursday: "There are no extradition proceedings in relation to [Mr Entwistle].
"In the circumstances it is not our role to comment on speculation regarding his whereabouts."
Earlier, the Home Office was unable to comment on reports that the computer engineer had returned to the UK or that US investigators had flown into Heathrow airport.
"I cannot confirm or deny anything connected to this investigation for operational reasons," a spokeswoman said.
According to the Boston Herald newspaper, four plainclothes state detectives flew to Britain on Wednesday night.
Ms Coakley said Mr Entwistle appeared to have left the US late on Friday or early Saturday morning local time and that his whereabouts were known.
She said: "He had contacted police at one stage and we have been in touch with him since."
She later added that Mr Entwistle had also been in touch with his wife's family.
The bodies of Mrs Entwistle and her daughter were found in bed at their home in the town of Hopkinton, near Boston.
The couple had moved into the property just 10 days earlier and had reportedly been due to host a dinner party on Saturday night.
However, when friends and family arrived, it appeared that no-one was at the house. Police were notified the following day.
The couple met through a rowing club when Mr Entwistle was studying electronic engineering with business management at the University of York.
They were married in 2003 and moved to the US shortly after the birth of their daughter.
Mrs Entwistle taught at St Augustine's Catholic High School in Hunt End, Redditch, Worcestershire, between 2002 and 2005.
The district attorney's office, which is overseeing the inquiry, said both deaths were being treated as "homicides".