Perrineau came forward last year to allege that in 2012, when she was 17 years old, Miller – whose production credits include King of the Hill and American Dad – took her and some friends to his home, where she later woke up with him "having sexual intercourse with me."
"At no time did I consent to any sexual contact with Murray", she told The Wrap, after filing a police report about the alleged assault.
Miller denied the allegations. Dunham and her co-show runner Jenni Konner issued a statement on the same day that the accusation against Miller emerged, which attempted to discredit Perrineau.
"While our first instinct is to listen to every woman's story, our insider knowledge of Murray's situation makes us confident that sadly this accusation is one of the 3 per cent of assault cases that are misreported each year," they said.
"It is a true shame to add to that number, as outside of Hollywood women still struggle to be believed. We stand by Murray and this is all we'll be saying about this issue."
Dunham retracted the statement shortly after it was published, after it caused mass uproar from critics calling out her feminism and accusing her of only defending white women who came forward with #MeToo stories.
In August, it was reported that Miller would not be charged.
A year later, in an open letter published in The Hollywood Reporter, Dunham has written a longer-form essay apologising to Perrineau directly.
In a brief sentence several paragraphs into the essay, she revealed: "I didn't have the 'insider information' I claimed but rather blind faith in a story that kept slipping and changing and revealed itself to mean nothing at all. I wanted to feel my workplace and my world were safe, untouched by the outside world."
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"There are few acts I could ever regret more in this life," she said, adding: "To Aurora: You have been on my mind and in my heart every day this year. I love you. I will always love you. I will always work to right that wrong. In that way, you have made me a better woman and a better feminist.
"You shouldn't have been given that job in addition to your other burdens but here we are, and here am I asking: How do we move forward? Not just you and I but all of us, living in the gray space between admission and vindication."