Depends on the state. For example, FL does not tax personal income. So no tax return for that state.
Yes you should even if the property runs at a loss to preserve that information for the time you sell the property ... if you have not been reporting the property and depreciation the state may not recognize it later.
The general rule is that rental income from a property located in State X is taxable by State X, as well as by the owner's state of residence.
If you abandoned your in-state domicile when you moved overseas, then you are no longer a resident of the state. However, as a non-resident, you are required to file a non-resident tax return that reports and pays income tax on locally sourced income (in-state income). A rental property in state A would be considered to be state A-sourced income.
Rental income from a property located in Indiana is taxable by Indiana. This website will guide you as to whether you should file as a resident, part-year resident, or nonresident:
https://www.in.gov/dor/individual-income-taxes/individual-income-tax-overview/