The state of Florida, like nearly every other state in America, subscribes to the "Castle Doctrine" which permits residents to use deadly force when attacked in their homes. See Weiand v. State, 732 So.2d 1044, 1051 (Fla. 1999) (holding that "[w]e join the majority of jurisdictions that do not impose a duty to retreat from the residence when a defendant uses deadly force in self-defense, if that force is necessary to prevent death or great bodily harm from a co-occupant."). In 2005, Florida sought to expand the "Castle Doctrine" beyond the confines of the home and passed statute 776.013 (hereinafter the "Stand Your Ground Law"), which provides in pertinent part:
A person who is not engaged in an unlawful activity and who is attacked in any other place where he or she has a right to be has no duty to retreat and has the right to stand his or her ground and meet force with force, including deadly force if he or she reasonably believes it is necessary to do so to prevent death or great bodily harm to himself or herself or another or to prevent the commission of a forcible felony. Fla. Stat. § 776.013(3) (2012).

The Stand Your Ground Law acts as an immunity to both criminal and civil liability once it is successfully raised at or before trial by somebody who has been accused of using deadly force. See Peterson v. State, 983 So.2d 27, 29 (App. Ct. 2008) (holding that "[t]he [Florida] Legislature finds that it is proper for law-abiding people to protect themselves, their families, and others from intruders and attackers without fear of prosecution or civil action for acting in defense of themselves and others.")...

CONCLUSION:
It is unlikely that a Florida court will hold that Florida's "Stand Your Ground" statute allows an armed Florida resident to claim self-defense in the shooting of an unarmed resident when the armed resident pursued and confronted the unarmed resident after being told by the police to stand down. Therefore, a Florida court will likely hold that the Stand Your Ground Law does not apply to the Trayvon Martin case.
Although not central to this discussion, it should be noted that the determination of whether the Stand Your Ground Law applies or not is ultimately one that is made by the Courts, not the police department. The standard criminal procedure is to arrest any defendant who kills someone else and detain him or her until a court or the state attorneys make a determination to release the defendant.