Six years ago, with crime rates at historic lows and Democratic progressivism on the rise, New York State began requiring prosecutors to turn over reams of evidence to defense lawyers well before a trial.

The goal was to level the playing field for criminal defendants, who often took plea deals without understanding the full scope of the case being built against them.

But many of the state’s district attorneys say that their offices have struggled to comply with the new requirements and blame them in part for an increase in case dismissals, which rose 22 percentage points in New York City.

They have urged state leaders to consider changing the so-called discovery rules, and have won over a powerful ally, Gov. Kathy Hochul.

The governor, a Democrat, is backing a measure that would ease the consequences for prosecutors if they do not share evidence in a timely manner. Her proposal would also let them redact information without a judge’s permission.

Ms. Hochul has said her plan will improve processing times and solve the problem of dismissals “based on technicalities that can prohibit justice to victims and the people of the State of New York.”