Acadia Healthcare, one of the country’s largest for-profit chains of psychiatric hospitals, has agreed to pay nearly $20 million to settle a federal investigation accusing the company of defrauding taxpayer-funded health insurance programs like Medicare and Medicaid, the Justice Department said on Thursday.

Prosecutors said that Acadia had held patients for longer than necessary and admitted people who didn’t need to be there. Once patients entered its facilities, the government said, Acadia failed to provide therapy and kept staffing dangerously low, leading to assaults and suicides.

Under the settlement, Acadia has agreed to pay the federal government as well as four states — Florida, Georgia, Michigan and Nevada — to resolve allegations that the company had violated state laws.

Tim Blair, an Acadia spokesman, said that the company had been cooperating with the government and did not admit any wrongdoing. He said that resolving the investigation “allows us to ensure our focus remains on providing quality care to our patients and their families.”

Acadia operates more than 50 psychiatric hospitals nationwide, and more than half of its revenue comes from government insurance programs.