My brother doesn't qualify as a dependent on my Federal return, but TurboTax MI state return counted him as a dependent. Is this correct?

That would depend on why he failed to qualify as a dependent on your federal tax return.

Briefly, the federal rules for claiming dependents fall into two categories:

Qualifying child

• They are related to you;
• They aren't claimed as a dependent by someone else;
• They are a U.S. citizen, resident alien, U.S. national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse or are filing a joint return only to claim a refund of withheld income tax or estimated tax paid;
• They are under the age of 19, or 24 if a full-time student;
• No age limit for permanently and totally disabled children.
• They live with you for more than half the year (temporary absences from your home, while living at school, still count as time living with you); and
• They didn't provide more than half of their own support for the year.

A new requirement this year is that each qualifying child dependent must have a Social Security Number, issued before the due date of your tax return (including extensions) to be claimed for the Child Tax Credit.

Qualifying relative

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They are related to you or lived with you the entire year as a member of your household.
• They made less than $4,150 in 2018.
• You provided more than half of their financial support.

It is entirely possible that your state has slightly different rules, so that a qualifying relative who, for example, failed by making too much income for the federal return might qualify on your state return if the state income standard is different.