BANGOR, Maine — The Maine Supreme Judicial Court heard arguments Wednesday in a case that pits the state’s need to investigate suspected criminal activity against the U.S. Constitution’s guarantee against unreasonable search and seizure.

It was the third and final day justices heard arguments in Bangor at the Penobscot Judicial Center. Since Monday, appeals in more than a dozen cases were considered by the state’s high court.

An attorney for the defendant, Ronald A. LaPlante, 53, of Bangor, argued that the court erred when it denied a motion to suppress evidence because the traffic stop that led to his conviction for drunken driving violated the Fourth Amendment.

An investigation of a noncriminal offense does not justify a law enforcement officer making a traffic stop without reasonable articulable suspicion, Zachary Heiden of the Maine Civil Liberties Union told the justices on LaPlante’s behalf.

William Entwhistle, assistant district attorney for Hancock County, argued that the officer was justified in stopping the defendant because LaPlante witnessed another motorist speeding, and civil speeding offenses are a sufficiently important public interest to justify an investigatory seizure of potential witnesses.

Justices fired questions rapidly at both attorneys and put forward possible compromises, such as ruling the stop itself legal to seek information but finding illegal the use of information obtained from the stop to file criminal charges.

Heiden rejected that premise.

“We need a ruling to clarify the stop,” he told the justices. “Without it, police could stop anybody for any reason.”

“If the stop is valid,” Entwhistle countered, “what is learned from that stop is fair game.”

LaPlante was stopped on Nov. 9, 2007, near the intersection of Routes 179 and 180 in Ellsworth by a Maine State Trooper, who asked if LaPlante had seen which way a driver in a red Pontiac the trooper suspected of speeding had gone. The driver of the car was caught on radar going 71 miles per hour in a 45-mph zone, according to court documents.

The trooper, according to briefs filed in the case, did not suspect LaPlante of breaking the law. During his conversation with LaPlante, however, the trooper began to suspect the defendant was driving while intoxicated and charged him with drunken driving.

The case was delayed until April 2009 because the trooper was deployed to Iraq, according to briefs.

LaPlante entered a conditional guilty plea pending the outcome of the appeal. If the justices rule against LaPlante, he would spend 60 days in jail and be on probation for two years. He already has paid the $1,400 fine, according to his attorney Jeffrey Toothaker of Ellsworth.

Justices also heard arguments Wednesday in the case of David Archer, 36 of Bangor. He appealed his conviction for attempted murder. He was sentenced last summer to 18 years in prison with all but 13 suspended after a jury found him guilty in January 2010 of trying to kill his ex-girlfriend in April 2008.

In his appeal, Archer’s attorney, Verne E. Paradie Jr. of Auburn, who did not represent the defendant at trial, argued that the testimony of Archer’s mother should not have been admitted because the statement was not made to the victim or anyone related to her.

Archer’s mother testified that her son, about six hours before the stabbing, said would kill his ex-girlfriend when he saw her with her new boyfriend.

Paradie also argued that medical evidence to prove the severity of the victim’s injuries should not have been admitted.

Susan Pope, assistant district attorney for Penobscot County, argued that Justice William Anderson, who presided over the trial, properly admitted all the evidence. Only one justice asked a question of her and not all the time set aside for arguments in the case was needed.