It is different for each state.
For NY, your wife will file a part-year return and may use the filing status as Married Filing Separate. This way only her income is calculated and taxed in New York.
For Ohio, you are required to file as Married Filing Joint. You will input her nonresident period into the Ohio return, and Ohio issues a credit for how much they would tax that portion of income that she earned while living and working in New York.
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