Ok, maybe I'm just completely dense, but I don't really understand the whole "domicile" concept. What is the difference between domicile and residency?
This is my understanding. All US citizens have to file Federal income tax returns.
Whether or not you file a state return depends on if your state is a domiciliary residence state and if your state has an income tax. Obviously, if you were a resident of a non-income tax state, you never filed state income tax returns and won't in thhe future. That's the easy one.
For all the other states, you have to figure out if they are a domiciliary residence state. This information is generally on the state's department of revenue website. If your state is one of these, you continue to file state income tax returns, unless you can prove that you became a resident of another state (look at the earlier list LisaE provided). Moving to another country doesn't get you out of this. The only way to get out of filing in that state is taking up residence in another STATE.
On the other hand, some states do not have domicile rules. For instance, my residence is in LA and it is a not domiciliary residence state. I will not have to file state income tax, in the future, because of this, regardless of the fact that I will still have ties to the state (like voting, bank accounts, etc.).