The U.S. Supreme Court refused last week to block the part of Obamacare that requires employers to provide insurance coverage for birth control.

Hobby Lobby Inc., an arts and crafts chain, objected that the mandate violates the owners' religious beliefs, The Hill reported last week.

While the Supreme Court refused to grant an emergency appeal, the court said the question of whether corporations have religious rights is unsettled and suggested the issue could eventually reach the high court, Lyle Denniston pointed out in the Constitution Daily.

Here's what Justice Sonia Sotomayor said in her ruling last week:

“This Court has not previously addressed [religious freedom] or free exercise claims brought by closely held for-profit corporations and their controlling shareholders alleging that the mandatory provision of certain employee benefits substantially burdens their exercise of religion.”

While it might sound weird for a corporation to be able to "practice" religion, Denniston notes the family-run corporations suing over the contraceptives mandate have said they want their business operations to reflect their personal convictions.

Another company suing over the mandate, K&L Contractors, argues that the company is an "alter ego" that allows its owners to express their religion under First Amendment.

While the right of corporations to express their religious beliefs is uncharted territory, the notion that corporations have rights under the Constitution isn't new.

In its controversial Citizens United ruling in 2010, the Supreme Court ruled corporations had a First Amendment right to spend freely on political campaigns.

And Justice Samuel Alito has pointed out that corporations like The New York Times also have a right to free speech.

Still, it's not clear whether the First Amendment exempts corporations, or people, from following laws that violate their religious beliefs.

In its 1990 decision in Employment Division v. Smith, the Supreme Court said the right to exercise religion freely doesn't relieve people of the obligation to comply with a "valid and neutral law," Wendy Kaminer has pointed out in The Atlantic.

"If religious objections to contraception and sterilization merit an exemption from federal law," Kaminer wrote, "then so could religious objections to hiring gay people or single mothers (or married ones, for that matter)."

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