No. Form 843 is a federal form and does not apply to a Detroit City return.
Detroit says, "If your City of Detroit allocation is less than 100 percent, please obtain a letter from your employer" to verify the amounts on the tax form and keep a work log. You do not have to send those but keep a copy for your records in case you are asked to produce them.
See the note at the bottom of Schedule W, Part 3: Wage Allocation for Nonresidents.
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