I have officially have establish Domicile in Fl but still have a NJ residence which I stay for less than 5 months (on and off) for the year. Am I non or PT NJ resident?

You don't say when you moved. In general, this is what NJ considers a nonresident.

 

You are a nonresident for tax purposes if:

 

• You did not maintain a "permanent" home in New Jersey; and
• You did maintain a "permanent" home outside of New Jersey; and
• You did not spend more than 30 days in New Jersey.

Also, you are a nonresident if:

• New Jersey was not your domicile, and you spent 183 days or less here; or
• New Jersey was not your domicile, and you spent more than 183 days here, but you did not maintain a "permanent" home here.

In some cases, a nonresident may be required to file both part-year resident and nonresident returns. If you were a resident of New Jersey for part of the tax year, earned income here, and also received income from a New Jersey source while a nonresident of New Jersey, you must file both part-year resident and part-year nonresident returns if your income for the entire year was more than the filing threshold amount for your filing status.

 

NJ NR

 

If you lived there part year, you will need to file a PY return and the dates should calculate the correct NJ portion.

Thanks. Does TurboTax allow you to enter multiple date ranges of when I am in NJ? I tend to go back and forth to that residence. 

It sounds to me like you are a New Jersey resident with a second home in Florida.