Emrah Bulatci was convicted three years ago of the first-degree murder of RCMP Const. Chris Worden in Hay River in 2007.
Bulatci shot Worden four times during a foot chase.
He will continue serving a life sentence with no chance of parole for 25 years.
The killer challenged more than a dozen rulings made by the original trial judge, including the admissibility of intercepted jailhouse conversations.
As usual, the Supreme Court gave no reasons for refusing to hear Bulatci's appeal.