Yeah, University of Michigan does provide scholarships based on merit. Here are some of them:

The Stamps Scholars Program
Total Worth: Full cost of attendance
Eligibility: Full cost of attendance
Minimum Criteria: Based on academic performance

Alumnae Council Scholarships
Total Worth: one-time $2,500
Eligibility: one-time $2,500
Minimum Criteria: Based on academic Performance
Separate application needed: Yes
Application deadline: February 15

University of Michigan provides aids at an average of 27050 per student meeting 92% of students need. 95% of students with need receive financial aid at an average of 19099 need-based grant. They also provide other scholarships including MUSIC Matters Scholarship Fund and SSGT Ergin V. Osman Scholarship Fund.