Yes, you will have to file tax return in both the States. You will report the income in IL and pay state tax in IL. Since you are resident of Missouri, you will report the income in Missouri tax return too but you will get a credit for taxes paid to IL so you will not be double taxed on the same income.
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Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.