American Ashley Olsen, whose naked body was found in her Florence apartment last week, was strangled with an object such as a rope or cord, according to initial autopsy results.
She was found by her boyfriend, Federico Fiorentini, a local artist, on Saturday after he had become worried about her whereabouts.
Fiorentini is understood to have told Italian police that they had fought a few days earlier, but has reportedly been cleared of involvement.
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According to NBC News, police removed several cords from Olsen's apartment in San Frediano, although they would not confirm if the murder weapon was among the evidence seized. Her phone had not been located, added investigators, and there was no sign of a struggle or of forced entry.
Italian prosecutor Giuseppe Creazzo said more time was needed to determine when the 35-year-old died. Chemical analyses of body tissue and fluid should help to narrow the time period, he added.
Olsen, from Summer Haven in Florida, was working in the fashion industry in Florence after leaving the US a few years ago to spend more time with her father, Walter Olsen, an art professor in the city.
"We are devastated that our precious Ashley has passed away resulting from a horrible and senseless crime," he said.
"She was a beautiful and creative young woman with a happy, exuberant and generous soul, and she loved her life in Florence, in San Frediano. We are heartbroken that she was taken from us."
Ashley Olsen murder in Italy sparks fear of another Knox saga
11 January
The apparent murder of an American expat in Italy has prompted fears of another Amanda Knox-style legal saga.
Ashley Olsen, 35, from Florida, was found dead in her Florence apartment on Saturday. She had bruises and scratches on her neck. Her pet beagle, Scout, was nearby and there were said to be no signs of a forced entry.
Police questioned her boyfriend – a local painter – over the weekend. They have yet to name any suspects.
Friends and expats in the area have expressed concerns that the case might follow in the footsteps of the Meredith Kercher murder case, which dragged on for years under the media spotlight.
Kercher, a British student, died in the Italian town of Perugia in 2007, although it was not until last year that the trials surrounding her death came to a close.
The legal battles began in 2009, when US student Knox and her then boyfriend Raffaele Sollecito were tried and convicted of the murder, verdicts that were later overturned by an appeal court. A retrial in 2013 again found them guilty before Italy's highest criminal court, the Court of Cassation, definitively cleared them both last March. Another man, Rudy Hermann Guede, from the Ivory Coast, is serving 16 years in prison for Kercher's murder.
One 17-year-old Florence resident told CBSNews that the Knox saga was the first thing she thought of when she heard of Olsen's death. "We've been through this terribly unresolved mystery with Amanda Knox," she said. "You never want it to get to that point."
Another American woman living in Milan told the Associated Press that Olsen's death "reignites the concern of justice, different policing and judicial systems and the different journalism styles between Italy and the US". Social media groups for expats in Florence have expressed similar views, adds AP.
The investigator in charge of the Florence Flying Squad is also "no stranger to high profile murder cases involving foreigners ", says the Daily Telegraph having led the investigation into Kercher's murder in 2007.
