As a US citizen or green card holder, you must report and pay federal income tax on all your world-wide income no matter where you live or earn the money.
If you maintain an abode (permanent residence) in a state, you generally must file and pay income tax in that state, even if you are temporarily living away from your abode. And there is no time limit on being "temporarily away", it depends on all the facts and circumstances. However, it is possible to change or abandon your abode, then you would not owe state income tax. For example, if you moved to Texas, you would owe no state income tax. We can give you more information about the concept of abode if you think that will help you.
