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if you were either a resident or a part-year resident of Illinois during the tax year; and you paid income tax to another state (city included) on income you earned while you were an Illinois resident, and the income subject to the other state’s (and city's) tax is included in your Illinois base income, and you did not deduct the income tax paid to the other state and city when you figured your federal adjusted gross income as shown on your Illinois tax return.

you are entitled to a credit for the income tax by both while an Illinois resident

you use Illinois schedule CR

for steps 1 and 2 

full year Illinois residents: In Column A of each line, except Line 15, enter the amounts exactly as reported on the corresponding line of your federal income tax return.
Part-year residents: In Column A of each line, enter the amounts as reported on the equivalent line of your Schedule NR, Column B.

for step 3

In Column A, enter the total amounts from your Form IL-1040. You must read the instructions for Column B to properly complete this step.

 

since NY rates exceed IL rates the credit will be based on the IL rates.