I am being asked by the state of IL to provide my CA state tax return to prove I lived there in 2015. Any help on how to get my CA state tax return from 2015?

You can't download the pdf file?  Sorry if you have the .tax2015 file you have to open it in the 2015 program.   But  you first need to download the state program to open it.  BUT Turbo Tax only supports the last 3 years so you can't get the state program.  

You could try the TaxPrinter service (not connected with Turbo Tax) to convert a .tax file to pdf at

http://www.taxprinter.com

I don't know if they do state.   They might be expensive and it is probably not safe to email tax returns back and forth.

See error 190

https://ttlc.intuit.com/community/bugs-and-error-messages/help/error-190-when-opening-file-in-turbotax-desktop/00/26443

Maybe you can get a copy from California FTB.  But they may be like the federal and only keep 7 years.

https://www.ftb.ca.gov/myftb/index.asp