You will still need to file taxes in both states but Turbo Tax will recognize that you paid state taxes in one of the states. Usually what happens is that you will be given a refund in the state you worked in and will need to pay taxes for the state that you didn't, for that 3-month period of time..
To avoid this next year, there is a reciprocal state agreement between Maryland and West Virginia. If you work in West Virginia and live in Maryland, you must file a form WV/IT-104R with your Human Resources Dept to avoid having state taxes withheld in the state of West Virginia. Here is a link that explains reciprocal agreements and i also will include a link to a pdf copy of the WV/IT-104R. Here is the the link to the copy to fill out and submit to HR.
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