The ruling does not mean that Ms. James will automatically receive the answers she is seeking. Mr. Trump and his children can invoke their constitutional right not to incriminate themselves, as Mr. Trump’s other adult son, Eric Trump, did when questioned by the attorney general’s office in October 2020. The Trump family can also appeal the decision.The judge’s decision followed a fiery virtual hearing in State Supreme Court on Thursday, during which lawyers for Mr. Trump and the attorney general made their cases. Several times, Mr. Trump’s lawyers became so heated that Judge Engoron and his law clerk had to call for a timeout — raising their hands in the shape of a T, a gesture more often seen at a sporting event than in a courtroom.Although Ms. James signaled in court papers that she had amassed significant evidence against Mr. Trump’s family business — she has accused the Trump Organization of engaging in “fraudulent or misleading” practices — she has said that she needs to question Mr. Trump and his children before determining her next move.Mr. Trump and his children sought to block the questioning, and Ms. James responded in a court filing last month, arguing that there was “heightened need” for testimony from the three family members. She said that by questioning them, she would be able to determine who was responsible for the misstatements and omissions that the company made in its financial documents.Because Ms. James’s inquiry is civil, she cannot bring criminal charges. If she finds evidence of wrongdoing, she can file a lawsuit against Mr. Trump, his company or others involved in the business. In last month’s filing, Ms. James said that her lawyers had not yet reached a final decision on a lawsuit but argued that “the grounds for conducting the investigation are beyond reproach.”On Monday, Ms. James released a letter in which Mr. Trump’s accounting firm, Mazars USA, declared that Mr. Trump’s financial statements from 2011-20 were not reliable. Mr. Trump provided those financial statements, which include various disclaimers noting that they are unaudited, to his lenders and at least one insurance company. They are central to both the civil and criminal inquiries into Mr. Trump.Mazars said in the letter that it had not “as a whole” found material discrepancies between the information the Trump Organization provided and the actual value of Mr. Trump’s assets, something that Mr. Trump’s lawyers asserted had effectively rendered the civil and criminal investigations “moot.”