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According to Florida statutes the person should register with the county.
Any person who shall have established a domicile in this state of Florida may manifest and evidence the same by filing in the office of the clerk of the circuit court for the county in which the said person shall reside, a sworn statement showing that he or she resides in and maintains a place of abode in that county which he or she recognizes and intends to maintain as his or her permanent home.
The attached link has more detail.
I hope this clarifies your question.