I paid tax in two states, can I get any of this money back?

Q: I moved from California to Massachusetts in July, continuing to work in Massachusetts for the same employer. Before I left I submitted a new W-4 changing my address. My company didn't change my location code until eight pay periods later. For those eight pay periods I paid tax in both California and Massachusetts. Is it possible to get any of this money back for both my state and federal returns? --Kathleen

The following answer was provided by Dona Lawson, CPA, Michael Taicher, PC.

A: I am assuming your income was earned in both states. You will need to file a part year return in each state claiming the income you earned in that state. You will then claim the withholding for each state. Any refund amount will be determined by your liability less your withholding.