Unfortunately, no. The only way for your son/daughter to be able to claim the MI Homestead Property Tax Credit for this off-campus apartment, would be if your child filed his/her own return independently.
Below I have included a link to Michigan's Department of Treasury Website- specifically the section on eligibility for the Homestead Property Tax credit.
http://www.michigan.gov/taxes/0,1607,7-238-43535_43538---,00.html
