An Oregon bakery found guilty of discriminating against a lesbian couple has appealed the ruling to the U.S. Supreme Court.

In June, the Oregon Supreme Court refused to review a lower court's ruling upholding a decision by the Oregon Bureau of Labor and Industries that found Aaron and Melissa Klein, owners of Sweet Cakes by Melissa in Gresham, guilty of unlawfully discriminating against the couple when they refused to make a cake for the women's commitment ceremony. The agency imposed a $135,000 fine on the Kleins.

Aaron Klein declined to make the cake for the women on January 17, 2013. Klein said he does not hate gays but that making a cake for a same-sex wedding would violate his faith. (At the time, Oregon had the nation's most robust domestic partnership law. Following a federal judge's ruling in May, 2014, Oregon became the 18th state to allow gay and lesbian couples to marry.)

The Kleins are represented by the Texas-based law firm First Liberty, which describes itself as “a national religious freedom law firm.”

On Monday, the group appealed its case to the Supreme Court, asserting a First Amendment right to turn away same-sex couples asking for wedding-related services.

Earlier this year, the Supreme Court ruled in favor of a Colorado baker who refused to sell a cake to a male gay couple for their wedding reception. (The couple married in Massachusetts because at the time Colorado did not allow such unions). The high court found that the state had an anti-religion bias, but it did not rule on the merits of the case.

(Related: Supreme Court narrowly sides with baker who refused gay couple.)

Four justices must vote in favor of taking the case for it to be accepted.