There are special rules for dependents. The following is from the MN instructions. page 12.
https://www.revenue.state.mn.us/Forms_and_Instructions/m1_inst_18.pdf
If I did not fully answer your question please give me some more detail.
As I put above a dependent does not get the full standard deduction and it is limited to formula I showed and that is why they own money.
I only filed a federal return to get a refund for all taxes paid not because I was required to file. The same applies to MN. I only earned $8,300 and I do not have to pay MN taxes because I did not go over the $10,650 minimum on page 6 of the instructions. I am only filing to get back the taxes I was not required to pay. Last year I received a full refund.
Page 6: Filing Requirement for Residents Who are not a Dependent