WASHINGTON — The “too big to fail’’ label is finally having its day in court.

A federal judge raised tough questions on Wednesday over regulators’ decision to designate the insurer MetLife as “systemically important’’ to the financial system.

Judge Rosemary Collyer focused on how a body of regulators, known as the Financial Stability Oversight Council, made its decisions about companies that could harm the economy, as well as whether regulators followed their own guidelines in the MetLife case.

“I’m trying to figure out if this is a reasonable way for this process to work,’’ she said in the US District Court for the District of Columbia.

MetLife sued the government in January 2015 after regulators determined the insurer was a “systemically important financial institution,’’ or a SIFI, that could damage the entire economy in times of distress. The company is being represented by Eugene Scalia, a partner at the law firm Gibson, Dunn & Crutcher and the son of Justice Antonin Scalia, who has accumulated a handful of decisive wins against the Securities and Exchange Commission and the Commodity Futures Trading Commission during the last decade.

While banks are subject to stricter supervision based on asset size under the Dodd-Frank reform law, regulators are empowered to look at insurers and other financial institutions based on a variety of factors, including how a firm is interconnected with other companies and the scope of existing regulation, when deciding whether it is systemically important. Designated firms are subject to stricter oversight by the Federal Reserve.

The financial oversight council has also labeled ­Prudential Financial and the American International Group, along with General Electric’s ­financial unit, GE Capital, as SIFI.

Collyer examined several aspects of the government’s defense of the MetLife designation. She took issue, for example, with the structure of the council, asking whether it has appropriate systems in place to separately gather the evidence and analyze the numbers about possible SIFIs and then fairly judge the firms.

There is “nobody neutral’’ in the process, the judge said.

MetLife has argued that the agency improperly imagined a situation in which the insurer was in financial distress and measured the predicted effect, as opposed to considering the probability that it would find itself on the brink of bankruptcy in the first place. The government, according to MetLife, initially said it would do the latter when looking at a firm’s riskiness.

Eric Beckenhauer, a lawyer for the Justice Department, sought to alleviate the judge’s concerns, arguing that there was no mandate that regulators could not blend their functions when making a designation. He defended regulators’ interpretation of the Dodd-Frank law and its own guidance document in the MetLife case.

Still, despite the sharp questioning, MetLife may face an uphill fight, given the courts are often inclined to defer to the judgment of regulators.

Collyer, who will decide the case, noted several times that the Dodd-Frank law asked regulators to designate institutions that “could’’ threaten the financial system, language that invites a certain amount of discretion.

“You can’t run away from it,’’ because the wording is in the statute, she said, adding that it’s “not a high bar.’’