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

Presidential Scholarship
Total Worth: $20,000-$24,000 per academic year
Eligibility: $20,000-$24,000 per academic year
Requirement for maintenance: Remain full time undergraduate student and a minimum cumulative GPA of 3.0
Separate application needed: No

Distinguished Scholar Awards
Total Worth: $15,000-$18,000 per academic year
Eligibility: $15,000-$18,000 per academic year
Requirement for maintenance: Remain full time undergraduate student and a minimum required GPA
Separate application needed: No

Charger Award
Total Worth: $10,000-$14,000
Eligibility: $10,000-$14,000
Requirement for maintenance: Remain full time undergraduate student and maintain required GPA
Separate application needed: No

University of New Haven provides aids at an average of 23746 per student meeting 60% of students need. 100% of students with need receive financial aid at an average of 20963 need-based grant. They also provide other scholarships including Federal Pell Grants and Dean’s Scholarships.