You can claim the property tax credit, even as a dependent, as long as you were a Michigan resident for at least six months in 2024 and had household resources under $69,700.
Many college students aren't residents of the state in which they attend school. If your permanent residence is in another state and you're only in Michigan temporarily for school, you will not qualify for this credit.
Household resources include financial support received from another person (such as your mom paying one month of your rent) as well as "nongovernmental scholarships, stipends, or grants paid directly to an educational institution". See the instructions to lines 24-32 of Form MI-1040CR.