Depending on which state you last lived in, the answer is "most likely."
"Depending on which state you most recently lived in before your move,
you may need to file a non-resident state income tax return even if you
are living abroad. Do not assume that since you have left the US you are
not obligated to file a state tax return. Each state has its own set of
rules about whom it considers a “resident” and their own minimum filing
requirements. Most states, but not all, also allow the foreign earned
income exclusion in determining taxable income.
Most states will allow you to be released from you residency status if you can prove your residency somewhere else for more than six months of the year.
Only four states make ending your residency very difficult:
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California,
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New Mexico
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South Carolina
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Virginia
If you moved from one of these states, it is unlikely you have been
released from your filing obligation. In each of these states you must prove
that you will not return to the state. If you cannot prove this, you
must file a state income tax return. They look at several different
factors to determine if you may return to the state at some time. These
factors among others include: property mortgages, leases, voter
registration, driver's license, and utility bills."
usexpattaxhelp.com
