No. Your Nevada car registration fee will be included on your California income tax return because of the way California computes tax for part-year residents.
Part-year residents pay state tax on the California percentage of a base tax amount that includes total 2020 income - total deductions.
For example if you made $100,000, split evenly between CA and NV, and had $20,000 in deductions, your CA base tax would be computed on $80,000 ($100,000-$20,000). Say that tax is $10,000. Your part-year CA tax would be 50% of $10,000 (the base tax).
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