The consultancy - which found itself at the heart of Facebook's controversial data sharing scandal earlier this year - was accused of improperly obtaining users' information.
As reported by the BBC, the latest proceedings are part of the ongoing process of closing down the firm and its UK parent SCL Elections, which started back in May.
The company has placed the blame for its closure on a "siege of media coverage", which it claims has driven away customers.
Cambridge Analytica has - in papers filed with a New York court - said it had assets of up to $500,000, and that it has debts somewhere between $1 million and $10 million.
Despite the company's closure and decision to lay off staff, regulators have made it clear that will still investigate how the firm used Facebook data.
The latest update comes after the social network said it obtained data on around 87 million users through a quiz on the site, which was then passed onto Cambridge Analytica.
The firm has been accused of using this for political campaigning, but the political consultancy has continued to maintain that it has done nothing wrong.