I am a full time college student living in Kansas. Last summer I had an intern job in Illinois June-August. Do I have to file taxes in both Kansas and Illinois?

[MarilynG1]

Yes, you should prepare a return for both states.  Prepare your Non-Resident Illinois return first.  If you don't owe any tax (or are not getting tax you paid refunded), you don't need to  actually file it, but you'll need to prepare it to know for sure.  

You will always file a Resident Kansas return, where you report ALL of your income.  Kansas then gives you credit for any tax you paid to Illinois (or any other state). 

Here's more info on How to File a Non-Resident State Return.