This needs to be addressed by a Florida attorney. Connecticut does not have reciprocity for carry permits.
Brian S. Karpe, Esq. (860) 724-6426 Note: This response DOES NOT constitute legal advice and therefore no specific action should be taken in reliance thereon. No attorney-client relationship is created through this response. You should speak to an licensed attorney in your state who is competent to answer your question before taking any action with regard to this question.