More than twenty people were arrested Thursday in Washington, D.C., on federal charges connecting them to a series of Medicaid and other health-care schemes that prosecutors say cheated taxpayers out of tens of millions of dollars.

Those charged are accused of running separate — and sometimes competing — schemes to bill the government for in-home health-care services that were not provided. A Bowie, Maryland, woman also was accused of racking up more than $75 million in billings after she had been barred from being a part of federal health-care programs.

According to the indictments, the alleged swindlers — who included operators and workers at home-care and nurse-staffing agencies — recruited Medicaid recipients to claim that they needed expensive in-home health care, even coaching them on how to exaggerate their symptoms to persuade doctors to sign off on treatment plans. The accused would then pose as the Medicaid recipients’ personal-care assistants, having them sign time sheets while they billed the government, according to the indictments.

“Doctors wrote prescriptions for these visits,” said Valerie Parlave, the assistant director in charge at the FBI’s Washington Field Office. “But no care was ever given.”

Those charged gave the Medicaid recipients a cut of the proceeds — usually a few hundred dollars at a time — and pocketed the rest, according to the indictments.

The alleged swindlers were able to take millions from the District’s Medicaid program — which is mostly federally funded but run by the city — although investigators were still calculating the precise amount. He said law enforcement officials were partially inspired to investigate the fraud when they noticed an unusual increase in the amount of money being paid out for personal-care services.

According to U.S. Attorney Ronald C. Machen Jr., in 2006, 2,500 Medicaid beneficiaries billed the government $40 million for personal care services. By 2013, 10,000 beneficiaries were billing the government for $280 million.

Prosecutors said that as part of the probe, they seized several luxury cars, including a 2013 Mercedes GL450 and a 2013 Porsche Panamera.