London (CNN) -- Investigators may not know what killed singer Amy Winehouse until they get results from lab tests on her blood and tissue, due in about two to four weeks, according to Scotland Yard Monday.
An autopsy was completed at St. Pancras Mortuary Monday afternoon, two days after the singer died in her London apartment.
"It did not establish a formal cause of death and we await the results of further toxicology tests," a police statement said.
An inquest into her death was opened Monday, the statement said.
"Inquiries continue into the circumstances of the death," London's Metropolitan Police, also known as Scotland Yard, said in a statement Sunday. At this stage, the 27-year-old's death "is being treated as unexplained and there have been no arrests in connection with the incident," police said.
The singer, beloved for her talent but infamous for erratic public behavior, arrests and drug problems, was found dead at her apartment in London on Saturday.
Winehouse's family said in a statement Sunday it "has been left bereft by the loss of Amy, a wonderful daughter, sister, niece. She leaves a gaping hole in our lives. We are coming together to remember her and we would appreciate some privacy and space at this terrible time."
"We are trying to come to terms with the death of a dear friend and colleague, the most amazing artist and talent," her management company, Metropolis Music, said Sunday. "We will always remember Amy as a vibrant, funny, caring young woman who made everyone around her feel welcome. We have lost a very special person, part of our family."
Her funeral will be held Tuesday, the singer's spokesman Chris Goodman said.
Sparse details are being released about the ceremony -- including exactly when and where it will occur -- though Goodman said "it will be a small, private event for a few friends and family."
Winehouse's soulful, throaty vocals brought the British musician stardom in 2007, but her troubled off-stage life -- chronicled in her Top 10 hit "Rehab" -- won her notoriety. Her death came less than two months after her latest release from a rehabilitation program and weeks after she was booed offstage by disappointed fans in Belgrade, Serbia.
Winehouse died at the same age as at least four other recent music legends. Jimi Hendrix, Janis Joplin and Jim Morrison each died of drug overdoses when they were 27. Kurt Cobain was 27 when he committed suicide, soon after his release from rehab.
Police were called to Winehouse's Camden Square apartment just after 4 p.m. Saturday in response to a report of "a woman found deceased," authorities said.
"Everyone who is involved with Amy is shocked and devastated," Winehouse spokesman Chris Goodman said. "Our thoughts are with her family and friends."
Her father, Mitch, got word of his daughter's death Saturday while in New York preparing for a Monday night show with his band at the Blue Note club, his publicist said. He immediately canceled the performance and caught a flight back to London, the publicist said.
Winehouse's official website carried nothing but a black-and-white photo of the singer.
On Saturday, a statement on the site said Winehouse was "withdrawing from all scheduled performances."
Her song "Rehab," in which she sang "They tried to make me go to rehab, I said no, no, no," helped form the public's view of Winehouse. She told CNN in a 2007 interview, "I don't care enough about what people think of me to conform to anything."
The London-born singer was a tattooed teenage rebel after she was expelled from a prestigious performing arts school. Her first album, "Frank," debuted in 2003, when the singer-songwriter was 19.
International success came with her 2007 album "Back to Black." She dominated the 2008 Grammys, winning five awards that night and delivering, via satellite from London, a strong performance of "Rehab."
Winehouse's volatile marriage to Blake Fielder-Civil took a toll on the singer's career. The couple divorced in 2009 after a stormy two years filled by drug addiction and arrests.
Winehouse's parents went public with their efforts to help their daughter, telling the London Telegraph in 2009 that she was on the road to recovery.
"A gradual recovery, which is good," Winehouse's father told the Telegraph. "With slight backward steps -- not drug backward steps, more drink backward steps if you follow my drift. I think that will be the pattern of recovery."
The organization that awards the Grammys issued a statement Saturday calling Winehouse "a dynamic performer and musician who seamlessly blended rock, jazz, pop, and soul and created a sound all her own."
"Her rich, soulful and unique voice reflected her honest songwriting and earned her a devoted fan following, critical acclaim, and the genuine respect and admiration of her musical peers," the Recording Academy statement said. "She will forever be remembered for her immense talent, and her music will live on for generations to come. Our deepest sympathies go out to her family, friends, and fans during this difficult time."
CNN's Bharati Naik, Denise Quan and Alan Duke contributed to this report.