Out-of-state rental apartment

[m2m]

Good morning.

Please - some help on below questions and any additional applicable information.

NJ resident owns rental co-op apartment in NYC.
1.  Is income reportable on NJ return?
2.  Is a NY return required even though the income amount may not be NY-taxable?
3.  How about if it is a loss, rather than income?
        a.  Still be good idea to file NY return, just to get it on record when apartment is sold?
        b.  Loss can be claimed on NJ return?

Thank you kindly.