I have a rental property in NY but I live in FL. After all expenses my rental income is negative. Do I still have to completely a NY tax form for negative income?

[ToddL]

If you had a loss on the NY rental property and no other NY income, you don't need to file a NY return. 

If you are a New York State  nonresident  you must file  Form IT-203,  Nonresident and Part-Year Resident Income Tax Return ... , if you meet the following condition:

You are a nonresident with New York source income and your New York adjusted gross income Federal amount column (Form IT-203, line 31) exceeds your New York standard deduction.  https://www.tax.ny.gov/pit/file/standard_deductions.htm

[Wil Ga]

Won’t the loss cary over if tax form is filed for the next tax year?

[JotikaT2]

In order to carryover any passive losses from year to year, you will need to file tax returns for each year, even if no tax is due.  This ensures the losses are reported and carried forward correctly as well as ensuring you get credit for any of those suspended losses when they are freed up in the future.

@Wil Ga