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.
