The chair of late Supreme Court Justice Antonin Scalia is seen draped with black wool crepe inside the Supreme Court in Washington on Feb. 16. (Carlos Barria/Reuters)

The Supreme Court resumed its work Monday without Justice Antonin Scalia — “our man for all seasons,” Chief Justice John G. Roberts Jr. called him — and then quickly discovered how difficult it might be to decide cases with what is now an ideologically balanced bench of eight.

With four consistent conservatives and four liberals, the factions appeared to take opposite views of a case that would loosen the rules for police to question and search suspects in high-crime neighborhoods, and drew the court into a discussion of Ferguson, Mo.

Tie votes after Scalia’s death Feb. 13 will uphold the ruling of the lower court, which in this case favored the defendant.

The court opened two weeks of oral arguments with Scalia’s high-backed leather chair at the right hand of Roberts draped in black.

“We remember his incisive intellect, his agile wit and his captivating prose,” Roberts said. “But we cannot forget his irrepressible spirit. He was our man for all seasons, and we will miss him beyond all measure.”

Whether the Republican-led Senate will confirm whoever President Obama nominates to fill the seat is shaping up as a monumental Washington political battle, with great implications for the presidential contest.

Roberts did not touch on the controversy. Instead, he read a brief summary of Scalia’s life, recalling his birth in New Jersey to parents of Italian descent, his graduation at the top of his class at Georgetown University and his honors at Harvard Law School.

As a lawyer in the Justice Department, Scalia argued one case before the Supreme Court in 1976 and won — “establishing a perfect record before the court,” Roberts said, to laughter.

Scalia was the Supreme Court’s 103rd justice when confirmed in 1986, and wrote 282 majority opinions.

“He was also known on occasion to dissent,” Roberts said to more laughter.

Scalia’s fiery opinions objecting to the majority were so legendary that some were collected in a book. He has said they were meant to influence law students, and he hoped they would lead to future outcomes more to his liking.

At the “appropriate time,” Roberts said, the court will hold its own memorial service, along with the bar.

“And now we turn to the business of the court.”

The first case was what Justice Ruth Bader Ginsburg described as a “dense” examination of the contracting laws involving the Department of Veterans Affairs.

But the second showed that finding the necessary five votes to decide a case may be difficult on the court of eight.

It involves Edward Streiff, who was arrested by Detective Douglas Fackrell in South Salt Lake City in December 2006. Fackrell was checking out an anonymous tip that a house there was being used for drug sales, and he observed the house for about three hours over the course of a week.

At some point, Fackrell decided he would question the next person he saw leave the house, and that was Streiff. Fackrell explained his purposes and asked Streiff for identification. He called in the information and found there was a warrant for Streiff’s arrest on a minor traffic violation. He arrested Streiff, searched him and found drugs.

But the Utah Supreme Court threw out the conviction, because Fackrell had no reasonable suspicion of Streiff that justified stopping him in the first place.

The ideologically divided justices took opposite views of the case.

Justice Sonia Sotomayor said upholding the police action would give officers too much power.

“What stops us from becoming a police state and just having the police stand on the corner down here and stop every person, ask them for identification, put it through, and if a warrant comes up, searching them?” she asked Utah Solicitor General Tyler R. Green.

She and Justice Elena Kagan brought up a Justice Department report on Ferguson, Mo., where federal officials found that an overwhelming number of residents had warrants for the arrests issued because of minor traffic violations.

“I was surprised beyond measure by how many people have arrest warrants outstanding, and particularly in the kind of areas in which these stops typically tend to take place,” said Kagan.

Green acknowledged that Fack­rell lacked reasonable suspicion to stop Streiff. But he said the defense has acknowledged that the arrest warrant was valid, and thus the arrest allowed.

Under the Supreme Court’s precedents, he said, “once the arrest is lawful, the search incident to it is lawful, and all the evidence gathered . . in any search is lawfully seized.”

If Sotomayor and Kagan were surprised by the number of outstanding warrants, Roberts was the opposite. “I was surprised how low they were — 323,000 is a big number, but that’s the entire state of Florida.”

When Joan C. Watt, representing Streiff, told the court that upholding the police action would send law enforcement on a “fishing expedition” to hope someone had a warrant, Roberts said an officer’s safety was a good reason for him to find out more about the person he was about to question.

Doesn’t it happen, Roberts asked Watt, that “an officer walks up to the car and they’re shot?” It does, she answered.

“It seems to me not wanting to get shot’s a pretty good reason” to check for a warrant, Roberts said.

Justice Samuel A. Alito Jr. said Watt was asking for a big change. “Can you give me one other example of a situation in which this court has held that the fruit of a lawful search must be suppressed?” he asked.

If the justices’ comments ultimately reflect a tie, the decision of the Utah Supreme Court would be upheld. But there would be no opinion and it would set no precedent for the rest of the country.

The case is Utah v. Streiff.