Most likely, Maryland will process the refund from your originally filed return and you should receive it within a couple of weeks. You then have until April 15th to pay the balance due for your amended Maryland return.
That being said, If you received a W2 after filing your returns, you also need to file an amended Federal return. Your federal return includes all of your income, from all states. Also, you mention that you moved to Maryland in December, so you will most likely need to file a return for the state you lived in from January through November in addition to your Maryland part-year return.
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