Nielsen entered a conditional guilty plea to four counts of murder last year, and was sentenced to life in prison for a bloody killing spree in western Maine.
IFhis lawyers persuade the court that his statements to police should have been suppressed, Nielsen can withdraw that plea.
On Tuesday, attorney Margot Joly told justices that Nielsen told a state trooper that he wanted an attorney, but was never granted one.
But Assistant Attorney General Donald Macomber said Nielsen’s statements were ambiguous and that he later told detectives several times that he wanted to tell them what happened.
Nielsen entered guilty pleas to the murders of 50-year-old James Whitehurst of Batesville, Ark.: 65-year-old Julie Bullard of Newry: 30-year-old Selby Bullard of Bethel: and 43-year-old Cindy Beatson of Bethel. They were killed over Labor Day weekend in 2006.