BEIJING—Months after the death of a Chinese man in police custody sparked public outrage, prosecutors dropped negligence charges against five police officers despite finding their actions had contributed to the death.

Friday’s decision means a high-profile case won’t go to trial, while authorities appeared set on also keeping it out of the court of public opinion. Censors deleted negative commentary around the decision on the popular Weibo microblogging service and barred searches for the dead man’s name. Users were also blocked...