Yes, based on those numbers, you will report a $700 loss for NY. Because a rental activity is a passive activity, it is likely not allowed unless you have passive income to which it can be applied. It can be carried forward to apply against future passive income, or be deducted when the property is sold.
Although it could be argued that with a loss you do not need to file a NY tax return for this year, I recommend doing so for purposes of accurately tracking your NY calculation of passive activity loss (PAL) carryforward amount (which can be different that you federal carryforward amount reported on Form 8582).
See NY Form IT-182 at this link for more information on how NY calculated PAL limitations and carryf....
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