WASHINGTON — The Supreme Court on Monday declined to hear an appeal from the owners of an Oregon bakery who were fined for refusing to create a wedding cake for a gay couple. In a brief order, the justices instead returned the case to lower courts in Oregon “for further consideration” in light of a decision last year in which the court ducked a similar issue in a case concerning a baker from Colorado.

The court’s action on Monday left still unresolved the question of whether many kinds of businesses, including florists, photography studios, calligraphers and tattoo artists, may discriminate against same-sex couples on religious grounds.

[Here’s how other battles over serving same-sex couples have played out in court.]

Lower courts have generally sided with gay and lesbian couples who were refused service, ruling that they are entitled to equal treatment, at least in parts of the country with laws forbidding discrimination based on sexual orientation. The owners of businesses challenging those laws have argued that the government should not force them to choose between the requirements of their faiths and their livelihoods, citing constitutional protections for free speech and religious liberty.

The new case started in 2012 when the owners of a bakery called Sweetcakes by Melissa refused to make a wedding cake for a lesbian couple, Rachel Bowman-Cryer and Laurel Bowman-Cryer. The owners, Melissa Klein and Aaron Klein, said doing so would violate their religious principles.