Washington (CNN) – The high-stakes fight over implementing parts of the troubled health care reform law will move to the U.S. Supreme Court in coming months, in a dispute involving coverage for contraceptives and “religious liberty.”

The justices agreed on Tuesday to review provisions in the Affordable Care Act requiring employers of a certain size to offer insurance coverage for birth control and other reproductive health services without a co-pay.

At issue is whether private companies and non-profits can refuse to do so on the claim it violates their religious beliefs.

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