Yes, you should file your Forms W-2 with the State of Illinois. However, you do not have to file your Forms 1099 but must maintain them for your records.

You can submit your Forms W-2 electronically at this website:

http://www.revenue.state.il.us/ElectronicServices/ElectronicW2.htm

You do not have to submit your Forms 1099 to the State of Illinois but per their regulations: "You must maintain withholding income tax Forms W-2, W-2c, W-2G, and 1099s (such as 1099-R or 1099-MISC), in your records for a period of three years from the due date or payment of the tax, whichever is later."