I have W2s for two states because my residency wasn't clear and I told my employer the wrong state. (I live abroad.) Do I need to file/pay state taxes in both states?

[KarenJ]

Hi.  Each state has different residency and domicile rules.  If you are a resident of one of the states and intend to return to that state at the end of your foreign assignment, you should continue to file resident returns for that state. 

If your employer also erroneously withheld state taxes for another state, you are going to need to file a nonresident return for that state to receive a refund on the taxes erroneously withheld.