At least two other women have had made similar accusations.
Dunham was in a five-year relationship with Jack Antonoff, which ended in December 2017.
The new parents are yet to share any pictures of their daughter on social media.
Multi Grammy-winning singer and songwriter had appeared on “The Voice” in 2016 where she performed her hit Into You.
“I was wiping my eyes and thanking him again and again,” Dunham, who always dreamed of having children, wrote.
"And jamo absolutely loves shooting! And the rate that he is processing the handling of them, he makes me proud." Hart wrote
