CONCORD, N.H. — A lawyer for a man convicted more than four decades ago of killing an 18-year-old New Hampshire woman urged the state Supreme Court on Thursday to grant his client a new trial.

Robert Breest denied fatally beating Susan Randall in February 1971 and tossing her partially nude body onto the frozen Merrimack River in Concord.

He has twice been denied parole because he refuses to admit to the crime and take part in sex offender treatment. He has attempted to clear his name through DNA evidence, arguing it would show Randall had a violent struggle with at least two men and contradicting claims that Breest acted alone or even that he was one of the killers.

A Merrimack County Superior Court judge rejected his request for a new trial in 2015, prompting an appeal to the state Supreme Court.

Addressing the court Thursday, Ian M. Dumain argued the lower court should have considered whether the new evidence would have resulted in a hung jury rather than an acquittal. Defense attorneys also want to introduce additional evidence that wasn’t part of the original trial.

They want to challenge assertions from state police that Randall’s coat was in Breest’s car, based on particles recovered from the car and coat. Citing a 2013 affidavit in documents submitted to the court, defense attorneys said an expert witness said the methods used to link the coat to the car have been deemed “unreliable and insufficient to support the conclusion.”

Dumain also wants to cast doubt on testimony from a now-dead convict, David Carita, who testified Breest admitted to him that he had killed Randall. They want to introduce testimony from John J. Kelleher, who would say New Hampshire police at the time asked him to testify that he was in the Middlesex House of Correction when Breest admitted the murder to Carita — something defense attorneys say Kelleher has denied.

Assistant Attorney General Elizabeth Woodcock argued against a new trial since the DNA test couldn’t rule out Breest as the person who committed the murder.

She also questioned why Kelleher wasn’t called as a witness at the original trial and cast doubt on his story that he was visited by state police officer.

Randall’s sister, Sally Hembree, said she would be devastated if Breest was granted a new trial.

“All it would take is for him to admit to the crime. He could have been out of jail 20 years ago if he admitted it. But he won’t,” she said. “It’s absolutely unfair (to have a new trial). All the people are dead now.”

Breest’s wife, Carol, said he deserves a new trial because he never committed the crime and shouldn’t be punished simply because his DNA is similar to that of the killer.

“I hope they grant him a new trial or release him,” she said. “He served a long time for a crime he didn’t commit. It’s been 44 years since they took my husband away. … I love him. He has always been true. He has always helped me raise the kids from prison.”

This story has been corrected to show the assistant attorney general’s last name is Woodcock, not Woodcook.