No, you do not need to file a Illinois tax return. MI and IL have tax reciprocity so residents are not subject to double taxation.
You do owe Michigan on these wages.
For more information, follow these links:
https://ttlc.intuit.com/questions/2895760-which-states-have-reciprocal-agreements
Intuit on
Tax Reciprocity
http://www.michigan.gov/taxes/0,4676,7-238-75545_43715-154059--,00.html
