Even as the investigation has heated up, it remains unclear whether the prosecutors will seek an indictment of Mr. Weisselberg, which would mark the first criminal charges stemming from the long-running financial fraud investigation into Mr. Trump and his family company. The investigation into Mr. Weisselberg focuses partly on whether he failed to pay taxes on valuable benefits that Mr. Trump provided him and his family over the years, including apartments and leased cars as well as tens of thousands of dollars in private school tuition for at least one of his grandchildren. In general, those types of benefits are taxable, although there are some exceptions, and the rules can be murky. For months, prosecutors working for District Attorney Cyrus R. Vance Jr., a Democrat, have sought to pressure Mr. Weisselberg into cooperating with their investigation into Mr. Trump, and any deal could turn the trusted executive into a star witness against the former president. For now, Mr. Weisselberg appears to have rebuffed Mr. Vance’s office and continues to work at the Trump Organization.