All I've been able to find on this is the paper "Environmental Impact and Relative Invasiveness of Free-Roaming Domestic Carnivores—a North American Survey of Governmental Agencies" [1] which looked at the impact of non-native domestic carnivores (dogs, cats, and ferrets) in the US and Canada.
It says this in the discussion section:
> Aside from an occasional “stray”, there were no reports of “feral (breeding)” ferrets; nor were there reports that of “free-living”, or “naturalized” ferrets anywhere in the continental United States or Canada, including California. More importantly, no jurisdiction reported ferrets impacting local (native) wildlife, including ground-nesting birds, or threatened, endangered and sensitive species.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5664037/
Edit: this comment seems quite controversial. In a few minutes it got several up votes, then quickly got twice as many down votes, then quickly returned to about even. I'm quite confused by this.