You won't need to file a Florida return. Like Texas, Florida does not have a state income tax. Thus, the income you are receiving from Florida is not taxed there.
Florida does, however, have a tangible property tax, which your LLC might have to file (but this is not on your personal return). If your LLC has over $25,000 in tangible property, they might want to do a tangible property return for the Florida county where the rental activity occurs.. Please see this website for additional information on the Florida tangible property tax: http://floridarevenue.com/property/Pages/Taxpayers_TangiblePersonalProperty.aspx
Again, though, the tangible property return is something the LLC/partnership would file, if needed, and not something that you as an individual will file.
[Edited 3/23/2019:16:55 PST]
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