Does a minor child have to pay states taxes and not get a refund?

Check the returns to see if he is identified as your dependent. If a person can be claimed as a dependent by another taxpayer, their standard deduction for 2022 is limited to the greater of: (1) $1,150, or (2) your earned income plus $400 (but the total can't be more than the basic standard deduction for your filing status).

As an example, a 15-year-old who works after school and earns less than $12,950 would owe nothing in Federal taxes. But, they could owe Michigan taxes.

You must file a Michigan Individual Income Tax return if you have income that would be included in federal adjusted gross income that exceeds your allowed Michigan exemption allowance(s).   Note: For the 2022 tax year, each Michigan personal and dependent exemption allowance is $5,000 plus $2,900 for each eligible special exemption.