Former President Donald J. Trump’s family business, which is already under indictment in Manhattan, is facing a criminal investigation by another prosecutor’s office that has begun to examine financial dealings at a golf course the company owns, according to people with knowledge of the matter.

In recent months, the district attorney’s office in suburban Westchester County, N.Y., has subpoenaed records from the course, Trump National Golf Club Westchester, and the town of Ossining, which sets property taxes on the course, a sprawling private club that is perched on a hill north of New York City and boasts a 101-foot waterfall.

The full scope of the investigation could not be determined, but the district attorney, Mimi E. Rocah, appears to be focused at least in part on whether Mr. Trump’s company, the Trump Organization, misled local officials about the property’s value to reduce its taxes, one of the people said.