You must a joint OH return if you file a joint federal return. In the "My Info" section edit your personal information. Indicate you lived in OH on 31 Dec and did not live in any other state. Edit your spouse's personal information and indicate he lived in WA on 31 Dec and did not live in any other state. This serves two purposes.
1. You will not be asked for a date of move to OH.
2. In the OH return interview you will see a page in the "Residency" section that shows you as resident and your spouse as non-resident.
Any income attributed to him in the federal interview will be non-OH source income. This will be used to calculate a non-resident credit on your joint OH return based on the proportion of income that is your spouse's and not in OH. This credit is automatically calculated in TurboTax based on your "My Info" and income entries.
Here is an OH reference. (See page 15 "Filing Status")
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