It depends on how the college or university provides health insurance. Fully insured health plans, meaning the college or university pays a premium to an insurance company in exchange for the insurer to pay medical claims, have to cover contraceptives without cost sharing. Self-insured student health plans, meaning the college or university pays medical claims itself, are not subject to the ACA and do not have to comply with the contraceptive coverage requirement.
However, a change in federal rules, permitted to go into effect after a July 2020 U.S. Supreme Court decision, allows a private college or university that has an objection based on “religious beliefs or moral convictions” to exclude some or all contraceptives from a student health plan. This issue is subject to further legal proceedings, but currently, student health plan coverage of contraception may vary depending on your school. Check with your student health plan administrator to verify coverage of contraceptives. (45 C.F.R. §§ 147.131 - 147.133).