Story highlights The case would be against a homeowner's association, says attorney Daryl Parks

Demonstrations are held in Washington, D.C., Virginia and Florida

Zimmerman's lawyer and former Gov. Jeb Bush say "stand your ground" doesn't apply in this case

Police say evidence and testimony on the night prohibited an arrest

Attorneys for the family of an unarmed Florida teen shot to death last month plan to pursue a civil case against a homeowner's association, the family's lawyer said Saturday.

Daryl Parks, attorney for the family of Trayvon Martin, spoke to board members of the National Association of Black Journalists (NABJ) about the case.

He said there is evidence that the Twin Lakes homeowner's association told residents who saw suspicious activity to call George Zimmerman if they could not contact the police, according to an NABJ statement.

Martin, 17, was killed February 26 as he walked to his father's fiancee's house in Sanford, Florida, after a trip to the convenience store. Police say he was shot by Zimmerman, a neighborhood watch volunteer who says he was acting in self-defense.

Martin was unarmed, carrying a bag of Skittles candy and an iced tea, according to police.

Protesters upset about Martin's death took to streets in cities across the country Saturday, with some questioning why Zimmerman has not been arrested. Other protests are planned for Sunday.

"There are inconsistencies in our U.S. laws that allow people to claim self-defense as a way to get away with murder," said CNN iReporter Jarvis Matthews. A student at Georgetown University, he sent video from a march in Washington, D.C.

Another demonstration was staged alongside a busy road in Virginia Beach, Virginia, where many of the protesters wore hooded sweatshirts like the one Martin had on when he was shot.

"In a nutshell I think this case is not being handled properly -- that is why we have so many protests. It was a senseless situation," said CNN iReporter Ron Campbell.

And in Sanford, Florida, a handful of members from the New Black Panther Party rallied and offered a $10,000 reward for Zimmerman's "capture."

"It's time for us, as black men, to take justice in our own hands. If you won't give us justice, we will have to take justice," said Florida organizer Mikhail Muhammad. "An eye for an eye. A life for a life."

The New Black Panther Party, which the Southern Poverty Law Center describes as a "virulently racist and anti-Semitic organization," is distinct from the better-known Black Panther Party, founded in the late 1960s.

The city of Sanford responded to the bounty offer by calling for "calm heads and no vigilante justice."

"Attempts by civilians to take any person into custody may result in criminal charges or unnecessary violence," it said in a statement.

Meanwhile, a lawyer for the man at the center of the death investigation said Florida's "stand your ground" law doesn't apply to the shooting that killed the teen.

"In my legal opinion, that's not really applicable to this case. The statute on 'stand your ground' is primarily when you're in your house," said Craig Sonner, Zimmerman's attorney.

"This is self-defense, and that's been around for forever -- that you have a right to defend yourself. So the next issue (that) is going to come up is, was he justified in using the amount of force he did?"

The 2005 law allows people to use deadly force anywhere they have a right to be if they have reasonable fear an assailant could seriously harm them or someone else.

It also eliminated a long-standing "duty to retreat" in the face of imminent harm, asserting that would-be crime victims have the right to "stand their ground" and "meet force with force" when attacked.

The case has sparked a national debate over the Florida law and concerns about racial profiling. Martin was black and Zimmerman is white Hispanic.

Florida Gov. Rick Scott appointed a special prosecutor, Angela Corey, to look into the case. She said her office will decide whether to charge Zimmerman, clear him or send the case to a grand jury.

The case has also prompted a U.S. Justice Department investigation, which is in the fact-finding stage.

The Sanford Police Department said officers were prohibited from arresting Zimmerman the night of the shooting because physical evidence and testimony supported his claim that he acted in self-defense in accordance with Florida law. The police department gave the explanation to City Manager Norton Bonaparte, who included it in a letter to the community about the case, posted on the city's website.

Sonner said he and Zimmerman have not discussed what happened the night Martin was shot, though he said Zimmerman has talked with authorities -- unaccompanied by counsel -- whenever they have asked him to do so.

Zimmerman said he was driving in his gated community when he saw Martin walking and called 911 to report a suspicious person.

Zimmerman told the dispatcher he was following the boy, but the dispatcher told him that wasn't necessary. Moments later, several neighbors called 911 to report a commotion outside, and police arrived to find Martin dead of a gunshot wound.

Sonner says his client was injured that night and went to the hospital with a broken nose and a serious cut on the back of his head.

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"This is not about self-defense," the Rev. Al Sharpton told a crowd in New York on Saturday. "This is about a man deciding somebody, based on who he was, was a suspect and that he would take matters into his own hands."

Sharpton, who attended a rally in Sanford earlier this week, promised a "spring offensive of non-violent protests" nationwide about the case.

Former Florida Gov. Jeb Bush, who signed the "stand your ground" bill into law, said Friday that he does not believe it applies to the case.

"Stand your ground means stand your ground. It doesn't mean chase after somebody who's turned their back," Bush said while visiting a university campus in Texas.

Sanford police said Zimmerman did not indicate a chase, telling them instead that "he had lost sight of Trayvon and was returning to his truck to meet the police officer when he says he was attacked by Trayvon," the police said in the letter posted by Bonaparte.

Sonner said he believes Zimmerman's life is in danger and has advised him to keep a low profile.

"This case is spinning out of control," he said. "I hope there's a way to rein things in so it doesn't become an issue of a racial battle. I hope that things come back so that there can be a time for justice and for healing and not for just skipping the whole judicial process and going straight to sentencing."