You will have to file a part-year resident tax return for both Ohio and New York. After you complete your federal tax return and you move to the State Taxes sections, both of your part-year state returns will be listed. Prepare the Ohio tax return first, then the New York tax return..
You will allocate your income to the state that you were a resident of when you received it. You mentioned that all of your income was from Ohio. If you earned all of the income before you moved to New York, you will allocate all of the income to Ohio and $0 to New York. If you earned some of the income after you moved to New York, you will have to allocate the amount you earned while in Ohio to your Ohio return and the amount that you earned while a resident of New York to your New York return.