Pacheco has also claimed Renner has a history of substance abuse, as well as verbal and emotional abuse, and that he was under the influence multiple times while he was caring for their daughter.
Renner has vehemently denied the claims and has instead accused Pacheco of having a drug problem.
A representative for the star told Page Six, "The wellbeing of his daughter Ava has always been and continues to be the primary focus for Jeremy.
"This is a matter for the court to decide. It's important to note the dramatisations made in Sonni's declaration are a one-sided account made with a specific goal in mind."
Renner and Pacheco are currently in the midst of a custody battle, with Pacheco asking for sole custody with monitored visitation for Renner.