If you have income from rental units in another state, and that state has income tax, then yes, you have to file a tax return in that state, in addition to filing a tax return in the state that you live in.
You have to file a resident tax return in the state that you live in, and a nonresident state in the other state that you have income from. The income from the other state is subject to tax by that state. All your income is subject to tax by the state that you live in, no matter where the income is from. Depending on what the specific states are, one state will give you a credit for the tax that you pay to the other state.
You might cause problems for yourself by using an address on your tax returns that is not in the state that you live in. The states will assume that you live in the state shown in the address on your tax returns. They will think that you are not filing properly, and have not paid the correct tax. You should use your actual home address on your tax returns.