(CNN) -

An autopsy on comedian Joan Rivers has been completed, but more studies will be needed to determine the cause and manner of her death, New York City medical examiner's office spokeswoman Julie Bolcer said Friday.

Rivers, 81, died in a New York hospital Thursday afternoon, a week after suffering cardiac arrest during a medical procedure, her daughter said.

Rivers had been on life support at Manhattan's Mount Sinai hospital, where she was taken after she stopped breathing at the Yorkville Endoscopy clinic on August 28.

Rivers was undergoing an apparently minor elective procedure at the clinic when she suffered cardiac and respiratory arrest, according to the New York Fire Department.

Paramedics took her by ambulance to Mount Sinai Hospital, about a mile from the clinic, where she was initially listed in critical condition.

The outpatient clinic is now being investigated by the New York State Department of Health, spokesman James O'Hara said.

No criminal investigations are currently under way in Rivers' death, according to several New York law enforcement officials. The state health department is investigating whether there was any malpractice by the doctors and their staff, the same officials said.

The Rivers family made very little information about her medical condition public, finally confirming Tuesday that she was on life support.

"My son and I would like to thank the doctors, nurses, and staff of Mount Sinai Hospital for the amazing care they provided for my mother," her daughter said. "Cooper and I have found ourselves humbled by the outpouring of love, support, and prayers we have received from around the world. They have been heard and appreciated.'

Melissa Rivers and her son Cooper have spent the past week by Rivers' hospital bedside, rushing there last Thursday when they learned of her illness.

"My mother's greatest joy in life was to make people laugh," Melissa Rivers said. "Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."

The clinic has not responded to repeated calls from CNN about the state's investigation.

Yorkville Endoscopy's website says it is an "ambulatory surgical center" that has been "approved by the Department of Health." The description of its accreditations is blank.

"Yorkville Endoscopy is a state of the art facility, staffed by highly experienced endoscopists whose mission is to provide safe and compassionate care to patients and their families," the website says.

Tributes from Joan's friends

The funeral for Rivers will be at Temple Emanu-El in Manhattan on Sunday, according to temple spokeswoman Elizabeth Fezrine. Details, including the time and if the public will be allowed to attend, are not yet known, she said.

Tributes to Rivers and her long career included one from former first lady Nancy Reagan, whose close circle of friends included Rivers.

"Joan Rivers was not only a dear friend, but one of the kindest and funniest people I ever knew," Reagan said. "I doubt there's anyone who hasn't laughed at her or with her until they cried. Today our tears are those of sadness. I know I join millions in saying, 'Thanks for the good times Joan, we will truly miss you.' My love and deepest sympathy go to Melissa and Cooper."

Former CNN host Larry King knew Rivers for 45 years. "She knew no boundaries," King said. "Everything was funny to her. You couldn't really object because she took no prisoners."

Donald Trump, who chose her as the winner on a season of "Celebrity Apprentice," said Rivers "was stronger at the end than she was at the beginning. She had unbelievable stamina."

Ryan Seacrest, who worked with her on E! shows, called Rivers "a trailblazer in so many ways."

Liza Minnelli said Rivers was "my dear friend."

"I will miss her but I will always remember the laughter and friendship she brought into my life," Minnelli said.

E! and NBCUniversal, producers of Rivers' TV show "Fashion Police," sent condolences to her family on "this incredibly sad day."

"For decades Joan has made people laugh, shattered glass ceilings and revolutionized comedy," the studio said.