The New York attorney general’s office is investigating whether a for-profit school founded by Donald J. Trump, which charges students up to $35,000 a course, has engaged in illegal business practices, according to people briefed on the inquiry.

The investigation was prompted by around a dozen complaints about the Trump school, which the attorney general, Eric T. Schneiderman, has found to be “credible” and “serious,” these people said, speaking on condition of anonymity because the investigation was not yet public.

The inquiry is the latest setback for a six-year-old company, known until last year as Trump University, that already faces a string of consumer complaints, reprimands from state regulators and a lawsuit from dissatisfied former students.