You owe state income tax on all your worldwide income if you are domiciled in the state. That essentially means the location of your permanent home. If you still have a home in your state that you plan to return to some day, your are probably still domiciled there. You can be temporarily away for a long time (years even) and as long as you maintain your residence with an intention to return, you are still domiciled there. You generally can't establish a new domicile unless you also take active steps to abandon your prior domicile.
For more information, we would need to what state, why you are living overseas, and other circumstances that would show where you are domiciled.
