No. You do not enter the state withholding for household employees on your tax return. The withholding is from the employee's pay and they get the credit for that on their tax returns. However, you likely did pay OH Workmen's Comp premiums and OH state unemployment taxes for your household employee (nanny). Those are part of your childcare expenses for the form 2441 Dependent and Childcare Credit. You enter those expenses in the "Deductions & Credits" section, the "Child and other dependent care" topic.
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