This is the Capitol Police patch (for Florida) when it was still housed under Florida's Department of General Services. One of the actions that then-Governor Jeb Bush took after the events of 9/11/2001, was to move the Capitol Police under the auspices of the Florida Department of Law Enforcement (see next patch). The patch also seems to pre-date the merger of the Florida Departments of Administration and General Services, which now forms the Department of Management Services.
This patch was one of quite a few that was found in Tallahassee Regional Operations Center's garage, and given to me. More regarding the history of the Capitol Police can be found here.