Federal prosecutors in Manhattan are investigating health and safety conditions, including lead problems, in New York City’s public-housing system, according to court documents and city officials.

Prosecutors in U.S. Attorney Preet Bharara’s office are investigating whether the New York City Housing Authority, the largest public-housing agency in the country, made false claims for payment to the federal government related to safety conditions at city housing complexes, according to court filings. The investigation began last fall, court records show.

In a letter filed Wednesday, prosecutors asked a federal judge to compel the city’s Department of Health and Mental Hygiene to produce information related to the investigation, including “documents reflecting complaints of unsafe, unsanitary, or unhealthful conditions in NYCHA public housing” and information about people with elevated levels of lead in their blood.

U.S. District Judge Deborah A. Batts ordered the health department to turn over records and information.

A spokeswoman for Mr. Bharara’s office couldn’t be reached for comment Wednesday night.