The top court released its decision Thursday morning.
In November 2009, Emrah Bulatci was convicted in the killing of Const. Christopher Worden in Hay River, about 400 kilometres south of Yellowknife, not far from the Alberta border.
Worden, 30, was gunned down while responding to a call for assistance in Hay River on Oct. 6, 2007.
Thursday's decision means Bulatci cannot appeal his conviction to any other level of court.
The Supreme Court was considering whether to hear an appeal to hold a new trial, but the application for leave to appeal was dismissed. As is normally the case, the court did not give a reason for its decision.
Bulatci's lawyers argued police illegally recorded conversations Bulatci had while he was in jail.
Conversations recorded secretly
The recordings were conversations Bulatci, age 25 at the time, had with his girlfriend and family members who were visiting him at the North Slave Correctional Centre in Yellowknife. Bulatci asked them for help silencing a witness in the murder case. Jurors heard excerpts of five hours of conversations that police recorded secretly.
His lawyers also argued the jury selection was done improperly. They said since Worden’s killing generated so much public attention, they should have been able to scrutinize potential jurors more.
Bulatci's lawyers brought the case to the Northwest Territories Court of Appeal in January.
The court decided at that time that the jury selection was fair and that the recordings were made legally. The court also found the judge’s decision to let the jury hear them was the correct one.
Bulatci was sentenced to life in prison with no eligibility for parole for 25 years. He is in a maximum-security facility in Edmonton.