George Zimmerman, 29, who has a mixed ethnic background but has been identified as white, has been charged with second-degree murder in connection with shooting Martin, an unarmed African American teenager.
The Florida jury began deliberations in Friday afternoon. They began a second day of deliberations Saturday.
LAPD sources said the department already has hefty deployments out during the summer months and there has been intelligence to suggest unrest would follow the verdict in the Los Angeles area.
In Sanford, Fla., where the trial is taking place, officials have urged calm after the verdicts are read.
"The lives of two families have forever been altered and our hearts and prayers go out to both," he said, noting that local authorities "want to ensure the proceedings are carried out without interruption."