Yes, for the State of Michigan, the rules are the same. Here what MI Dept of Treasury says:
"The Michigan Department of Treasury follows the Internal Revenue Service (IRS) guidelines for estimated tax requirements. Based on the IRS estimated income tax requirements, to avoid penalties for failure to make estimated tax payments, your total tax paid through credits and withholding must be:
90% of your current year's tax liability,
or 100% of the previous year' liability,
or 110% if your previous year's adjusted gross income is more than $150,000 ($75,000 or more for married filing separate)."
