A New York City Council plan to decriminalize certain low-level violations—such as public urination or drinking alcohol in public from an open container—has sparked intense debate among state and city officials about how these so-called quality-of-life offenses should be treated by police and the courts.

But a path to a possible compromise appeared to be emerging Monday, officials said, as the state’s top judge voiced support for moving some of these offenses to civil court.

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