Wages form w2 - Should Box 16 have $0 and Box 17 still have the withholding if no work was conducted in that state, but tax was withheld?

Ex. Total Fed. Income earned $10,000, State of employment has $10,000 in Box 16 and has withholding.  A second W2 was issued for State of residence with $7,000 in Box 16 and has withholding.  No work was conducted in the State of residence, but tax was withheld.  Should Box 16 have $0 for Box 16 and still have the withholding in Box 17?