Investigation of a Shoplifting Incident

My question involves criminal law for the state of: Illinois

This question is more out of curiosity, than anything else. My ex recently attempted to steal a couple of Cliff bars from a gas station (yeah, seriously). When the cashier noticed, she pulled them out of her purse, placed them on the counter, and ran off into her car. Her and whomever she was with at the time then sped off.

I get a note in my mailbox from an officer of that city, asking me to give him a call regarding the incident. He received my contact information because of the car (my name is currently on it, lesson learned). I told him I haven't seen the ex in 3 months, don't have any contact information or address for her.

So I'm curious; would they put a warrant out for her arrest?

They certainly could do so. One of the risks you accept when you choose to commit a crime is uncertainty about whether or not you will be prosecuted. She will have to wait and see what happens.