On your federal tax return you do not file as a resident of any particular state. You do not designate your residency on your federal tax return.
When you file a state tax return you file as either a resident, nonresident, or part-year resident of that particular state. Each state has its own definition of a resident for income tax purposes. Since the states have different definitions, it's possible to be considered a resident of more than one state.
Since Florida has no individual income tax, you would never be filing a Florida tax return, so you do not have to determine whether you are a Florida resident.
If you file a New York tax return, you can't just choose whether you want to file as a resident or nonresident. You have to file based on your actual residency status according to the New York definitions. You can find the New York definitions of resident, nonresident, and part-year resident on the Income tax definitions page of the New York Department of Taxation and Finance web site.
