The credit for taxes paid to another state is automatically calculated in your account when you add a Nonresident return to your already created Resident Michigan return if you pay taxes to both Delaware and another state. If you qualify for the reciprocal agreement, you will need to remove the automatic calculation. Please see this article for information on how to do this.
Michigan may request a copy of the other state's tax return before processing the return. For more information, please see Michigan.gov website here.