If you have nonresident rental losses and this is your only source of nonresident income/loss, you have no filing requirement in that nonresident state. However, you may want to consider filing a return anyway so that you can establish with your nonresident state that the rental property produced a passive loss (which can be carried forward and used against future passive income). Some states still require rental losses to be reporting. This will vary by state.
You will still need to include your rental activities (income or loss) on your federal and resident state tax returns.
Thanks, so do I file taxes on where the partnership address is or where the investment is? For example, I have an multifamily apt investment that generates passive income in Little Rock, AK however the partnership LLC is registered in Monsey, NY. Do I file the state non resident form for New York?