Alphonso David, the governor’s chief counsel, said in an interview the investigation would be done in good faith, pointing to the progress the administration had made reducing the number of black inmates in solitary confinement. The governor will grant the inspector general’s office unfettered access, Mr. David said, as well as the necessary resources.

Mr. David, who has worked with Mr. Cuomo on civil rights issues for a decade, said that for him, this was personal. “As a black man,” he said, “I’m not going to look the other way if the evidence shows that the corrections department is applying discipline disproportionately to black and Latino men.”

The state investigation was prompted by a report in The New York Times last week documenting racial disparities in the prison disciplinary system. An analysis of 60,000 disciplinary cases from 2015 showed that black and Latino inmates were punished at twice the rate of white inmates at some prisons, sent to solitary confinement more often and were held there longer. At Clinton Correctional Facility, near the Canadian border, where only one out of the 998 guards is black, the disparity was particularly striking: Black inmates were nearly four times as likely as whites to be sent to isolation and were held there for an average of 125 days, compared with 90 days for whites.

No details have been released about how the investigation will be conducted. But based on a past federal lawsuit by advocates challenging the use of solitary confinement in New York prisons, it is possible to identify several avenues investigators may well take.

The first step would be to do their own statistical analysis. It took The Times nearly a year and several requests through the Freedom of Information Law to obtain sufficient data for its investigation, and even then, the state rejected some requests.