Assistant Chief Coroner Ed Winter said the the 32-year-old's exact cause of death would have to wait until the results of an autopsy -- scheduled for Monday or Tuesday.
He said her family is cooperating with the coroner's investigation, and authorities are looking into her medical history, but that her death "appears to be natural."
"In this time of sadness, the family thanks you for your love and support," a rep for Murphy said. "It is their wish that you respect their privacy."
Cedars-Sinai Medical Center Spokeswoman Sally Stewart told the Associated Press the actress died at 10:04 a.m. Sunday.
Los Angeles Fire Department spokesman Devon Gale says crews responded to a call at 8 a.m. Sunday from the house she lived in with her British screenwriter husband, Simon Monjack.
TMZ reported Murphy's mother found the actress unconscious in the shower, and was in full cardiac arrest when paramedics arrived at the house. Her mother reportedly told first responders Murphy had a history of diabetes, according to the celebrity Web site, adding they couldn't confirm if the actress did have the condition and whether or not it contributed to her death.
Neighbor Clare Staples said she saw firefighters working to resuscitate the actress Sunday morning. She said Murphy was on a stretcher and "looked as though she was dead at the scene."
Murphy's husband, wearing pajama bottoms and no shoes, appeared "dazed" as firefighters tried to save her, Staples said.
"It's just tragic," she added.
Murphy's father, Angelo Bertolotti, said he learned of her death from his son, the actress's brother, and was stunned.
"She was just an absolute doll since she was born," Bertolotti said from his Branford, Fla., home. "Her personality was always outward. Everybody loved her -- people that made movies with her, people on a cruise -- they all loved her. She was just a regular gal."
He said he hadn't heard much about the circumstances of Murphy's death. Bertolotti divorced her mother when Murphy was young and hadn't seen Murphy in the past few years. He said he used to be in the mob and served prison time on federal drug charges.
"She was just talented," Bertolotti said. "And I loved her very much."
Born Nov. 10, 1977 in Atlanta, Murphy grew up in New Jersey and later moved with her mother to Los Angeles to pursue acting.
Her career started in the early 1990s with small roles in television series, commercials and movies. She is best known for parts in "Girl, Interrupted," "Clueless" and "8 Mile."
Her on-screen roles declined in recent years, but Murphy's voice gave life to numerous animated characters, including Luanne Platter on more than 200 episodes of Fox's "King of the Hill" and Gloria the penguin in "Happy Feet."
She is due to appear in Sylvester Stallone's upcoming film, "The Expendables," set for release next year.
Her role in "8 Mile" led to more recognition, Murphy told The Associated Press in 2003. "That changed a lot," she said
Murphy credited her mother, Sharon, with being a key to her success.
"When I asked my mom to move to California, she sold everything and moved out here for me," Murphy told the AP in 2003. "I was really grateful to have grown up in an environment that was conducive to creating and didn't stifle any of that. She always believed in me."
She dated Ashton Kutcher, who costarred with Murphy in 2003's romantic comedy "Just Married."
Kutcher tweeted Sunday morning about Murphy's death: "2day the world lost a little piece of sunshine," Kutcher wrote. "My deepest condolences go out 2 Brittany's family, her husband, & her amazing mother Sharon."
FoxNews.com's Hollie McKay and the Associated Press contributed to this report.