A 77-year-old woman and her two adult sons were found dead in their home on Friday.
They were discovered with slit throats and blunt force wounds, but there was no sign of a break-in.
Police think the deaths may be connected to Friday's "blue moon", an unusual astronomical event.
A "blue moon" is a nickname for a second full moon within one calendar month. They can occur once every three years.
No arrests have been made, but police said they had identified a person of interest in the case.
Police described the crime scene as "very complex" and said the bodies had been positioned.
Escambia County Sheriff David Morgan said the victims - Voncile Smith, John William Smith and Richard Thomas Smith - were known to be "very reclusive, very secretive''.
Richard Smith worked at a nearby military base, but Mr Morgan said the case was unrelated to "national security elements".
Florida authorities are calling a recent triple murder in Pensacola a "ritualistic killing" and believe the suspect had ties to witchcraft.