"TurboTax also offers TurboTax Easy Extension, an online tool that allows you to file extensions for both your federal and state tax returns."
If you are certain that you cannot file your Illinois return by the deadline, you do not need to file for an extension. You will automatically receive a 6-month extension of time to file your return (not to pay). The extended tax return due date is October 15, 2019. If you expect to owe income taxes, you should submit your payment with payment voucher Form IL-505-I, Automatic Extension Payment for Individuals, by April 15, 2019. If you efiled your return and are making a payment by check or money order, you must complete a Form IL-505-I on efile.com. If you are making a payment by credit card, a Form IL-505-I is not needed. If you are making an automatic extension payment, you also must use Form IL-505-I unless it is made electronically. Use efile.com and prepare an Illinois tax return to find out what your Illinois state income tax payment will be.
https://www.efile.com/efile-illinois-income-tax-return-file-il-state-taxes-forms-refund/#extension