Directed by Lynn Shelton, who wrote, directed and produced 2009 Sundance award winner Humpday, the film also stars Rosemarie DeWitt (Mad Men, Rachel Getting Married) and Mark Duplass.
The plot centres on two recently-bereaved sisters, played by Blunt and DeWitt, who invite Duplass's character to stay with them at their family's remote cabin.
Blunt recently admitted that a joke about pubic hair helped DeWitt to cry tears of laughter for a scene in the film.
She also divulged that she was "starstruck" upon meeting US President Barack Obama for the first time.
Your Sister's Sister hits US theatres on June 15 and is released in the UK on June 29.
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Watch the trailer below: