Zimmerman, a neighborhood watch volunteer in the gated neighborhood, The Retreat at Twin Lakes, shot Trayvon dead while defending himself, he told Sanford police.
The Brevard-Seminole State Attorney's Office has asked the Florida Department of Law Enforcement to investigate.
Zimmerman has not been arrested, causing an outcry from the black community, activists and other citizens.
The New Black Liberation Militia, a self-styled black survival group, has announced that it plans to make a citizens arrest of Zimmerman next week, the Associated Press reported.
It quoted Najee Muhammad, a group leader, saying, "We'll find him. We've got his mug shot and everything."
Natalie Jackson, a lawyer for the Martin family, said she does not support the threat, but also cannot control them.
"There are people out there with their own agendas," Jackson said. "It's nothing we condone."
Zimmerman has moved out of his Sanford home because of death threats, according to his father, Robert Zimmerman.
Meanwhile, a hearing in Sanford will be held at 10 a.m. Monday for the family's request to release 911 calls linked to the shooting. Police have not released those records, saying they are part of the ongoing investigation.
A student protest is also scheduled Monday outside of the courthouse from 8 a.m. to noon.
People from around the nation have signed a petition on Change.org to call for the prosecution of Zimmerman. By Friday afternoon the online petition had collected nearly 250,000 signatures.
firstname.lastname@example.org or 407-420-5620
Trayvon Martin's father: Family 'betrayed' by Sanford police
Family's attorney says he may file complaint against Sanford police for witness intimidation, tampering and obstruction of justice.
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