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The NAACP called for the opening of a civil rights case against Mr. Zimmerman in an online petition addressed to Attorney General Eric H. Holder Jr.

Civil rights leaders, including the Revs. Jesse Jackson and Al Sharpton, urged peace in the wake of the verdict. Mr. Jackson said the legal system “failed justice,” but violence isn’t the answer.

But not all the protesters heeded those calls.

In Oakland, Calif., some angry demonstrators broke windows, burned U.S. flags and started street fires. Some marchers also vandalized a police squad car and used spray paint to scrawl anti-police graffiti on roads and Alameda County’s Davidson Courthouse.