You own a home in NC but still own a home in Illinois. Do you have to file a state tax return in Illinois to recoup your Illinois real estate taxes?

No. You only need to file a state return in states where you have earned income as designated on your W-2 form or where you had self-employed income. Now, realize that you cannot recoup real estate taxes but can use them as a deduction on your federal income tax return without regard to which state the property is located.