No - You will just enter your Federal K-1 under the federal section. The IL K-1 would only be used if you are not a resident of IL and need to file an IL nonresident state income tax return.
To enter K-1 information in TurboTax, log into your tax return (for TurboTax Online sign-in, click Here and click on "Take me to my return") type "k-1" in the search bar then select "jump to k-1". TurboTax will guide you in entering this information.
If you are required to file an IL nonresident state income tax return, then when you are doing the apportionment of the K-1 amounts from the federal return to the IL nonresident return, you will only allocate the amounts as show on your IL state K-1 as being IL sourced.
You will include the full amount of the K-1 on your resident state return and if you also had to file an IL nonresident state return, you will be able to claim a tax credit from the IL return on your resident state return.
For IL nonresident, you must file Form IL-1040 and Schedule NR if
- you earned enough taxable income from Illinois sources to have a tax liability (i.e., your Illinois base income from Schedule NR, Step 5, Line 46, is greater than your Illinois exemption allowance on Schedule NR, Step 5, Line 50), or
- you want a refund of any Illinois Income Tax withheld in error. You must attach a letter of explanation from your employer.
So if your IL-source income does not make you have an IL tax liability, you have no IL filing requirement.
Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return.
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)