"I always felt connected to her as we shared a very special experience in our lives together.
"I feel love in my heart for her - and hope she is at peace. This is truly sad."
Murphy left the production of indie film The Caller earlier this month. Her agent said she had quit because of "creative differences".
Going to California
Born in Atlanta, Murphy grew up in New Jersey but moved to Los Angeles with her mother to pursue acting.
Murphy was married to British screenwriter Simon Monjack
"When I asked my mom to move to California, she sold everything and moved out here for me," Murphy once said.
"I was really grateful to have grown up in an environment that was conducive to creating and didn't stifle any of that."
She started her career with recurring roles in TV series including Blossom, Party of Five and Sister, Sister, but came to attention as Tai Frasier - the "tragically unhip" slacker given a makeover by Alicia Silverstone's character, Cher.
Her most acclaimed role came opposite rapper Eminem in his biopic 8 Mile.
Speaking to the BBC about that film, she said: "What I love is the way it explores the willingness to get out of where you are, and the fact that you actually can make it, no matter what."
Murphy's other movie appearances included Girl, Interrupted, Sin City and Riding In Cars With Boys.
Her on-screen roles declined in recent years but Murphy voiced characters for the hit US television series King of the Hill and animated movie Happy Feet.
She is due to appear in Sylvester Stallone's film, The Expendables, set for release next year.
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