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. Self-insured student health plans, meaning the college or university pays medical claims itself, do not have to cover contraceptives. Also, non-profit religious universities can object to covering contraceptives on religious or moral grounds under federal law however, their insurer or third-party administrator must still accommodate contraceptive coverage and cover contraceptives at no cost to you.
Generally, student health plans have to cover contraceptives. However, a recent change in federal rules allows a college or university that has an objection based on “religious beliefs or moral convictions” to exclude some or all contraceptives from the student health plan. However, this exemption is being legally challenged and has not yet become effective. (45 C.F.R. § 147.131)