@WC21 You are correct on both. Even if your NRA spouse lived with you, tax law does allow you to claim Head of Household if your spouse is not electing to be treated as a resident alien. However, you cannot receive Earned Income Credit, which is why you still must report that you are filing separately. And you are using the correct TurboTax technique (the program is not well designed to handle this): use a dummy SSN, print it out, white out the dummy SSN anywhere it appears on the tax return and write in "NRA".
If your spouse has next to no income, however: Have you considered filing jointly and electing for your spouse to be treated as a resident for tax purposes? If you do so, you would likely have to file to apply for an ITIN for your spouse, but it is the most advantageous filing status available. Just presenting as something to consider.
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