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A lawyer for Trayvon Martin's parents said Wednesday new video showing the teen's killer George Zimmerman after their deadly clash, but without the head injuries he claims were inflicted upon him in the scuffle, was "the smoking gun" for those seeking to have him arrested.

The CCTV footage, released Wednesday, shows Zimmerman climbing handcuffed out of a police car and engaging with officers after he killed Martin, 17, on Feb. 26 in Sanford, Fla.

Not obviously visible are the broken, bloody nose and head wound that he claimed he sustained from being punched by Martin and having his head slammed into the sidewalk during their scuffle.

Zimmerman has said he shot Martin in self-defense after being attacked -- a claim backed by some witnesses, but contested by others.

Lawyer Benjamin Crump, appearing with Martin's mother Sybrina Fulton and father Tracy Martin on CNN's "Piers Morgan Tonight" Wednesday, said the video showed "there was some kind of conspiracy to sweep Trayvon Martin's death under the rug."

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Separately, he said in a statement, "This certainly doesn't look like a man who told police only an hour or so earlier he suffered a broken nose and had his head repeatedly smashed into the sidewalk.

"It only bolsters our claim that George Zimmerman was not beaten to the point that he feared for his life, as he had indicated. This armed vigilante needs to be arrested immediately for the murder of Trayvon Martin."

Reacting to comments made earlier by Zimmerman's friend Joe Oliver -- who said the 28-year-old would never be the same after the incident, was struggling to sleep, cried for days afterward and was now depressed -- Fulton said simply, "If I had killed an individual, I'd be crying too."

She added, "I believe George Zimmerman hunted my son like an animal."

And in relation to Oliver's claims that Zimmerman was not a racist, Tracy Martin said his son's killer may not have been a racist, "but George Zimmerman did racially profile Trayvon Martin."

Martin was walking from a 7-Eleven to the home where he was staying with his father in a gated community outside Orlando on Feb. 26 when Zimmerman, a neighborhood watch volunteer, phoned 911 to report that the black teen, who was wearing a hoodie, looked suspicious.

Despite being told by a police dispatcher not to follow Martin, Zimmerman left his vehicle to go after him. Martin was speaking by phone to his girlfriend as he walked and told her he was scared because someone was following him.

The two clashed in circumstances that remain unclear, which led to Zimmerman shooting the unarmed Martin and killing him.

Though he was taken into police custody that night, he was never formally arrested and has not been charged with any crime.