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Mr. Zimmerman’s brother, Robert Zimmerman Jr., said Sunday that the federal government already has conducted an exhaustive check of the Zimmerman family and found no evidence of hostility toward any ethnic group.

“We welcomed, actually, that investigation through the FBI when they originally started investigating George,” he said on CNN. “They’ve investigated, I think, about three dozen of his closest friends and acquaintances. And there is not any inkling of racism. It doesn’t do anybody good right now” to talk of new charges.

He added that groups such as the NAACP need to “cool their jets” and that “agitation doesn’t help us” in the aftermath of the trial.

It’s unclear whether the Martin family will publicly push for civil rights charges. Speaking on ABC on Sunday, the family’s attorney, Benjamin Crump, said they will “continue to fight for the legacy of their son” and also will consider a civil lawsuit against Mr. Zimmerman.

He did not address the family’s position on possible federal charges.

Such federal civil rights cases are somewhat rare but not unprecedented. While some legal analysts have said new charges essentially would amount to double jeopardy for Mr. Zimmerman, the federal government in the past has stepped in when a jury cleared defendants in cases involving perceived racism.

The precedents began with federal civil-rights cases being brought against segregation-era Southerners for killing blacks, a crime for which local juries were reluctant to convict. Several Los Angeles police officers were punished under federal law after being acquitted in 1992 of state crimes in the Rodney King beating, a verdict that prompted riots that killed more than 50 people.

In 2009, the Justice Department also brought hate-crime charges against two young Pennsylvania men involved in the beating death of an illegal immigrant. The two men, Derrick Donchak and Brandon Piekarsky of Shenandoah, Pa., were acquitted of murder charges in a county court earlier that year.

But that verdict led to an outcry from civil rights leaders and the Hispanic community, who argued that the victim, Luis Ramirez, was targeted solely because of his ethnicity. In 2011, Piekarsky and Donchak were convicted in a federal court of hate crimes and depriving the victim of his civil rights. They were sentenced to nine years in federal prison.