The Broadway star, best known for voicing Elsa in the Disney animation Frozen, made the comment as she promoted her new television movie Beaches – a remake of the 1988 film which starred Bette Midler.
Asked by a journalist which songs made her cry, Menzel replied: “You'd think because I'm a singer I listen to a lot of music, which I do, but there's certain music that I think is so devastatingly beautiful that it's too painful to listen to some times.
“There's this Meshell Ndegeocello album, Bitter, that I just can't listen to. It's so good. It makes me just want to slit my wrists.“
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Idina Menzel has been criticised for joking that a music album made her want to slit her wrists
Jessica Cruz, executive director of the National Alliance on Mental Illness (NAMI) California, told the Press Association: “Self harm and suicide is a very serious situation. Some people may not realise the impact of that type of statement.
It's so good. It makes me just want to slit my wrists
“It shows a lack of education around the pain families and individuals go through and further stigmatises mental health.
“It's joking about self harm when self harm is not a joke.“
David Bain, executive director of NAMI's Sacramento branch, added: “It's treating the issue without the true weight that suicide carries with it.
The Broadway star, best known for voicing Elsa in the Disney animation Frozen
“It's not an appropriate metaphor. She needs to consider the impact of her statement.”
But the Trevor Project, which helps young people from the LGBT community at risk of suicide, defended Menzel and said she was “expressing her appreciation of the emotional impact” of Ndegeocello's music.
Steve Mendelsohn, the charity's interim executive director, said: “While the Trevor Project believes her choice of words could have been better, we also firmly believe that Idina did not mean to imply that she would harm herself nor did she intend to encourage self-harm or suicidal tendencies in anyone else.”
Menzel, 45, has previously been quoted as joking about self harm.
In an interview with the New York Times in 2014, the Tony Award winner described seeing billboards of TV shows in which she failed to get parts, before adding: “It's like, take me home and just slit my wrists now.”
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Walt Disney provided Mickey Mouse's trademark falsetto voice for almost 20 years, before his hectic schedule – and reportedly his smoker's voice – meant he could no longer continue.
That same year, in an interview about her Christmas Wishes album, she told the Metro newspaper: “I suppose if Christmas makes you depressed this album might make you want to slit your wrists.”
Menzel has reprised the role of CC Bloom in Beaches, the character played by Midler in the original 1988 tearjerker.
The former Wicked star defended the number of film and TV show remakes, saying “there are only so many stories we can tell”.
She added: “I think there are people who are so excited, who love the movie and can't wait to see another incarnation of this film.
“Then there are people who will never be happy with the fact we're doing it and they don't have to watch it.
“We think we did justice to it.”
* Beaches airs on Lifetime on Sunday, March 12 at 9pm.