The U.S. Supreme Court has declined to hear an appeal by a Christian family-owned pharmacy in Washington that refused to sell contraceptives to women because of their deeply held religious beliefs.

In a decision issued on Tuesday, the High Court denied the appeal made on behalf of Ralph's Thriftway, a local grocery store and pharmacy in Olympia, Washington, owned by the Storman family for over 70 years.

The denial prompted Justice Samuel Alito to issue a scathing dissent, saying the "case is an ominous sign."

"If this is a sign of how religious liberty claims will be treated in the years ahead, those who value religious freedom have cause for great concern," Alito said. He was joined by Chief Justice John Roberts and Justice Clarence Thomas in the dissent.

With its ruling, the High Court has allowed a July 2015 ruling by the 9th U.S. Circuit Court of Appeals that upheld a Washington state regulation which states that "pharmacies have a duty to deliver lawfully prescribed drugs or devices to patients and to distribute drugs and devices . . . in a timely manner consistent with reasonable expectations for filling the prescription."

In 2007, the Washington Pharmacy Commission issued a new rule that prohibits pharmacies from referring customers who want to purchase Plan B contraceptive for religious reasons.

However, the commission allowed pharmacies to refer customers for other reasons.

In a decision in the original case in February 2012, a U.S. District Court in Tacoma, Washington, ruled that the 2007 rules "are not neutral, and they are not generally applicable."

"They were designed instead to force religious objectors to dispense Plan B, and they sought to do so despite the fact that refusals to deliver for all sorts of secular reasons were permitted. The rules are unconstitutional as applied to Plaintiffs," the court said.

But on appeal, the decision was reversed.

In 2014, the U.S. Supreme Court allowed certain businesses to refuse compliance with the Obamacare law, which requires companies to provide employees with insurance that covers contraceptives, according to Reuters.

The Stormans are devout Christians who view emergency contraceptives as abortion drugs.

"The dilemma this creates for the Stormans family and others like them is plain: Violate your sincerely held religious beliefs or get out of the pharmacy business," Alito said.

A total of 38 state and national pharmacy associates had asked the Supreme Court to take up the case.

Alito said evidence showed that Washington's rule was adopted due to "hostility to pharmacists whose religious beliefs regarding abortion and contraception are out of step with prevailing opinion in the state."

"Americans should be free to peacefully live and work consistent with their faith without fear of unjust punishment, and no one should be forced to participate in the taking of human life," said Kristen Waggoner, a lawyer with the Alliance Defending Freedom (ADF), which represents the Stormans.

Despite the decision, the Stormans said they are fully committed to honouring God in all they do.

"I don't know what the end result's going to be. But it's clear we're here for a purpose. I'll just ride this ship and do the right thing and believe God's going to use that for His glory," Kevin Stormans said, according to ADF.