BEIJING—Public outrage flared over a decision by Chinese prosecutors to drop criminal charges over the death of a researcher in police custody—an unusual display of middle-class anger over a perceived lack of official accountability.

Criticism has been building in the days since Beijing prosecutors said Friday that they won’t pursue negligence charges against five police officers despite finding that their “improper” actions had contributed to the death of 29-year-old Lei Yang in early May.

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