Zimmerman, 28, turned himself in at a county jail Wednesday after special prosecutor Angela Corey announced he would be charged in the case.
Prosecutors outlined their murder case in court papers, saying the neighborhood watch volunteer followed and confronted the black teenager after a police dispatcher told him to back off.
The brief outline, contained in an affidavit filed in support of the second-degree murder charges, appeared to contradict Zimmerman's claim that Martin attacked him after he had turned away and was returning to his vehicle.
In the affidavit, prosecutors also said that Martin's mother identified cries for help heard in the background of a 911 call as her son's. There had been some question as to whether Martin or Zimmerman was the one crying out.
It's been six weeks since Martin was shot and killed. Zimmerman has never disputed that he pulled the trigger, but has said it was done in self-defense citing Florida's "stand your ground" law.
During the brief appearance Thursday, Zimmerman stood up straight and wore a gray prison jumpsuit. He spoke only to answer "Yes, sir,'' after he was asked basic questions about the charge against him.
Zimmerman is charged with second degree murder, meaning prosecutors don't believe he intended or planned to kill Martin.
Some legal experts had expected Zimmerman to face a lesser count of manslaughter and say a prosecutor will face steep hurdles to win a murder conviction.
As his case plays out in the courts and in the court of public opinion, Florida's now controversial "stand your ground" law, which allows the use of deadly force anytime a person feels threatened, will be judged as well.
"I think what's going to be on trial here is not just George Zimmerman, but the 'stand your ground law,'" said attorney Ronald Fischetti. "I think that's what's going to be the issue in this case."
On Wednesday, New York City Mayor Michael Bloomberg spoke out against the Florida law.
"You cannot have a civilized society where everybody can have a gun and make their own decisions as to whether somebody is threatening or not," Bloomberg said. "There's no civilized society that I know, no democracy, that has these kinds of laws. Only in America where we have more guns than people."
Speaking Thursday on "CBS This Morning," Zimmerman's attorney Mark O'Mara said he plans to eventually seek to have his client released on bond.
"He's frustrated. He's tired. He's stressed. So, we just need to sort of take it one day at a time," O'Mara said.
At Zimmerman's court appearance, the judge said he found probable cause to move ahead with the case and that an arraignment would be held on May 29 before another judge.
Meanwhile, the head of the National Association for the Advancement of Colored People discussed the case during a visit to Hartford.
Benjamin Jealous, the NAACP's national president, said the organization is upping its efforts to curb racial profiling across the country in response to the high-profile case.
Jealous said the NAACP has recently pushed the U.S. Senate to hold hearings on racial profiling, and they will take place next week. He said his organization is also working at the state level.
(TM and Copyright 2012 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2012 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)
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