If your state taxes personal income, then you are required to report all income from all sources to your state too. If that includes income earned in another state, then it's taxability in your home state will depend on any reciprocal tax agreements that may (or may not) exist between the states involved.

Note that this has nothing to do with property taxes you may be required to pay to a state, or the tangible personal property tax you may be required to pay  the state on non-real estate rental property. Those have nothing to do with income tax, and we do not deal with that here.

If you're asking if state taxes are a deductible expense on your federal return, then in most cases the answer is yes. The program will deal with this for you automatically. But you have to actually complete the state return first, before the program "knows" if you have anything on the state return, that is deductible on your federal return.

If you had to file a second state return because rental property was located there, the tax you paid is not deductible as a rental expense, but the fee you paid to have that state return prepared is. Is this a special state tax rather than the normal state income tax? If so, please let me know which state.