A qualifying child must live with you, or your spouse if filing a married filing jointly tax return, in the United States for more than half of the year to qualify for the credit. So long as the primary applicant lives in Washington for the required 183 days during the tax year, then a child can still qualify if they live with the spouse outside of Washington for more than half the year and meet the other qualifying child requirements. Visit Qualifying Child Rules | Internal Revenue Service (irs.gov) for information on the qualifying child requirements.