Federal prosecutors have joined a state investigation into possible fraud by Charles J. Hynes, the former Brooklyn district attorney, signaling that he could now be facing federal charges with longer prison terms.

Assistant United States attorneys from New York’s Eastern District are coordinating with an investigation by the state attorney general, Eric T. Schneiderman, who began his inquiry after a city report suggested Mr. Hynes had used more than $200,000 in public funds for a consultant to his re-election campaign. The report, by the Department of Investigation, said the misuse of funds could amount to larceny.

But the involvement of federal prosecutors exposes Mr. Hynes to an increased range of potential charges, including federal program fraud, a felony in which someone at an agency commits fraud, embezzlement or bribery, and the agency receives over $10,000 of federal money in a year. In 2013, Mr. Hynes’s last year as district attorney, the office estimated it would receive $1.3 million in federal funds. The felony carries a prison sentence of up to 10 years.

Federal prosecutors also have more ways to pursue corruption cases than state prosecutors do. For instance, if someone conducting fraud uses email or calls someone in another state as part of the scheme, federal prosecutors can bring a wire fraud charge, which can carry a prison term of up to 20 years.