(CNN) -

The outpatient clinic where comedian Joan Rivers suffered cardiac arrest during a procedure last week is being investigated, a health official said Thursday.

Rivers was on life support and died at a New York hospital Thursday afternoon, a week after suffering cardiac arrest during a medical procedure, her daughter said.

"She passed peacefully at 1:17 p.m. surrounded by family and close friends," Melissa Rivers said in a statement.

Rivers was taken to the hospital after she stopped breathing at the Yorkville Endoscopy clinic last Thursday.

In addition, the New York medical examiner office "will be investigating the death of Joan Rivers," spokeswoman Julie Bolcer told CNN.

The New York State Department of Health is "investigating the matter," spokesman James O'Hara told CNN.

The length of the investigation will depend on how complicated the case becomes, O'Hara said.

Rivers, 81, 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 listed in critical condition.

Daughter Melissa Rivers confirmed Tuesday that her mother was on life support. She revealed Wednesday that Rivers had been moved from the intensive care unit to a private room, "where she is being kept comfortable."

A Rivers statement on Sunday said that the family was "keeping our fingers crossed."

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.