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That was a quote from the new york department of taxation and finance. New Jersey says:

 

This New Jersey Division of Taxation website states:

 

Credit for Taxes Paid to Other Jurisdictions

 

If you are a New Jersey resident with income from sources outside New Jersey, you may be eligible for a credit on your New Jersey tax return. You may qualify for a credit if you paid income or wage tax on the same income in the same year to both New Jersey and to another jurisdiction outside New Jersey.

 

To avoid double taxation, in the NJ return look for  Credit for Taxes Paid to Other Jurisdictions.