No.
Please see the PIT-RES Instructions on page 9. "Enter taxes paid to other states (net of credits). (Exclude city wage and county taxes paid directly to county)." (in the worksheet on page 9).
Also, "NOTE: Taxes paid to a political subdivision of a state cannot be claimed as a credit. The District of Columbia is classified as a “State” for the purpose of this credit and, therefore, taxes paid to the District of Columbia can be claimed as a credit on Line 12."
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