The top judge in New York has proposed radically overhauling the way grand juries in that state investigate police shootings and other fatal encounters, calling the current system “a relic of another time” and saying that judges, not prosecutors, should oversee the process. His suggestion this week came in response to nationwide protests that followed the decisions of grand juries in New York and Missouri not to indict police officers involved in two high-profile deaths.

“Let’s face it,” Jonathan Lippman, chief judge of the State of New York, said in his annual State of the Judiciary speech on Tuesday, “able and dedicated prosecutors and the grand jury process cannot win in these inherently incendiary situations. Damned if you do and damned if you don’t, no matter how strict the adherence to fairness and the rule of law.”

After grand juries did not indict police officers for the deaths of Eric Garner (an unarmed New York man who died after being placed in a chokehold by an officer) and Michael Brown (an unarmed 18-year-old shot and killed by an officer in Ferguson, Mo.), outraged protesters demonstrated across the country. One demand brought up in Missouri and New York involved the officials overseeing the grand juries, with protesters arguing that special prosecutors should be appointed to investigate incidents in which police officers use force.

Lippman’s proposal goes beyond that idea, instead saying that judges should take a much more active role in the grand jury process, going so far as to be physically present during the proceedings and to ask questions of witnesses.

“This puts the ultimate responsibility for the grand jury where it belongs — with the court — and it largely removes any negative perceptions about the grand jury process in these cases of great public interest,” said Lippman, who said he was submitting legislation for his proposals.

He also argued against the secrecy involved in the process, still a contested issue regarding the grand jury that considered Garner’s death. A judge recently heard arguments for releasing the testimony and evidence presented to that jury, though no decision has been announced.

Lippman proposed that when grand juries opt not to indict, the grand jury proceedings should be made public for cases where the subject matter is publicly known, the person being investigated has been publicly named and when there is “a significant public interest” to releasing the information. Otherwise, he argued, the public is left to speculate about what happened and why.

Responding to Lippman’s remarks, the head of New York City’s largest police union criticized the idea of creating a new method of investigating police officers.

“Judges already have a duty and responsibility to review all aspects of grand jury investigations, including instructions for deliberations given by prosecutors,” Patrick J. Lynch, president of the Patrolmen’s Benevolent Association, said in a statement. “They already have the authority to alter any ruling that they find does not meet the requirements of law making the suggested legislation unnecessary. The rule of law should apply evenly and fairly to all without exception. There should not be a separate system of justice for police officers.”

Lippman is the latest voice in New York to weigh in on how best to handle police shootings. Gov. Andrew M. Cuomo (D) said last month he wants to appoint independent monitors to investigate every time a police officer kills an unarmed civilian and that officer is not indicted by a grand jury. New York Attorney General Eric T. Schneiderman has also asked Cuomo to let his office investigate and prosecute cases involving unarmed people killed by police.