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DENVER — The Colorado Court of Appeals will hear arguments Tuesday in the case of a same-sex couple that has sued a Lakewood bakery.

The couple wanted the bakery to make them a wedding cake, but the owner of the shop refused.

The case has been ongoing for the past couple of years. The gay couple has already won their case before the state’s Civil Rights Division. But the owner of the bakery is appealing on religious grounds.

The couple first approached Masterpiece Cakeshop in Lakewood in 2012. David Mullin and Charlie Craig wanted a cake for their upcoming wedding.

But owner Jack Phillips told the couple it was against his religious beliefs to make a cake for a same-sex ceremony. He said he had turned down other couples as well on religious grounds.

So the couple took their case to the Colorado Civil Rights Commission. In May 2014, the commission found the bakery was in violation of the state’s Anti-Discrimination Act.

In 2013, Judge Robert N. Spencer of the Colorado Office of Administrative Courts ruled Phillips broke discrimination laws.

The case takes on new importance in light of the U.S. Supreme Court’s ruling in favor of same-sex marriage last month.

A couple in Oregon recently won a similar case against a bakery and was awarded $135,000.