Lotus Entertainment will finance, produce and handle international sales at the American Film Market.
Sheridan will direct from her own script. She received an Academy Award nomination along with her sister Naomi Sheridan and father Jim Sheridan for 2002's "In America."
Winehouse died of alcohol poisoning in 2011, five years after rising to international fame with her "Back to Black" album.
Kirsten Sheridan said: "Amy's music is felt so deeply by the audience because it was deeply personal. Her vulnerability was her strength. She was called many things -- a diva, a lost soul preyed upon by tabloids, a tortured genius; our aim is an innovative, emotional and life-affirming approach as we go through the looking glass into her life and art."
Rapace is best known for starring in "Prometheus," along with the Swedish film adaptations of the Millennium series: "The Girl with the Dragon Tattoo," "The Girl Who Played with Fire" and "The Girl Who Kicked the Hornets' Nest."