The trailer has also been released online and shows Zaldana as Simone, who died in 2003, and it appears the actress has altered her face for the role with makeup.
Saldana took to Twitter to share a message, writing, "I'll tell you what freedom is to me- No Fear... I mean really, no fear." #NinaSimone."
The official Simone family Twitter fired back with ".@zoesaldana Cool story but please take Nina's name out your mouth. For the rest of your life."
The "Official Twitter for the Estate & Legacy of Dr. Nina Simone" added in another tweet Wednesday night that, "Hopefully people begin to understand this is painful. Gut-wrenching, heartbreaking, nauseating, soul-crushing. It shall pass, but for now..."
This isn't the first time the Simone family has had a problem with Saldana's casting. In 2012, Simone’s daughter, Simone Kelly, spoke to The New York Times and was open about her concerns.
“My mother was raised at a time when she was told her nose was too wide, her skin was too dark. Appearance-wise this is not the best choice," she said of Saldana, adding she is a fan of the actress, but not for this role.
Meanwhile, the family is not alone with their concerns.
"The people behind the project weren’t my cup of tea. The director was fine, but there was a lot of mismanagement, which is why we’re still here three years later," Saldana told Latina magazine last year about the film's delayed release. "I either finish this movie and release it, knowing that we did the best we could, or this movie goes away. I pray that somebody tells her story and they do it amazingly well. And then I’ll just put this to rest."
Saldana's rep and the production company Ealing Studios have not responded to ABC News’ requests for comment.
"Nina" is set to be released on April 22.