Mark L. Rienzi, a lawyer at the Becket Fund for Religious Liberty, which represents Wheaton, said, “The court rightly recognized that Wheaton’s religious community should be allowed to practice its faith free from crushing government fines.”

The college objected to coverage of intrauterine devices and so-called morning-after pills, saying they were akin to abortion. Many scientists disagree.

The court did not announce how most of the justices had voted, which is typical when it issues unsigned opinions. In the Hobby Lobby case on Monday, Justice Stephen G. Breyer joined Justices Sotomayor, Ginsburg and Kagan in dissent.

The majority opinion there, written by Justice Samuel A. Alito Jr., seemed to suggest that the forms could play a role in an arrangement that was an acceptable alternative to having employers pay for the coverage. Under the arrangement, insurance companies that receive the forms pay for the coverage on the theory that it costs no more to provide contraception than to pay for pregnancies.

On Thursday, the court’s majority said all Wheaton had to do was notify the government in writing “that it is a nonprofit organization that holds itself out as religious and has religious objections to providing coverage for contraception services.”

The difference between a form sent to insurers and plan administrators on the one hand and a letter sent to the government on the other mattered, the college told the justices, “because it believes, as a religious matter, that signing the form would be impermissibly facilitating abortions and is therefore forbidden.”