SANFORD, Fla. -- A Florida judge says there's probable cause to move ahead with the second-degree murder case against George Zimmerman.

The neighborhood watch volunteer made his first court appearance today in the shooting death of Trayvon Martin. Zimmerman said little during today's hearing. The judge set an arraignment for May 29th.

His lawyer said afterward that he's concerned that the case has been handled in the public eye up to now. Mark O'Mara said, "It's really supposed to happen in the courtroom." He deflected questions about evidence in the case and about Zimmerman's mental state.

Zimmerman resurfaced yesterday to turn himself in after weeks in hiding. He has admitted shooting the unarmed teen, but has said it was self-defense.

His lawyers could still keep the case from going to trial. Under Florida law, his lawyers have a relatively low legal standard by which to show that he acted in self-defense. One Florida defense attorney says there's a "high likelihood" the case could be dismissed by a judge before a jury gets to hear it.