Arguments were heard Tuesday in a Yellowknife courtroom.
A jury found Emrah Bulatci guilty in November 2009 in the first-degree murder of RCMP Const. Chris Worden two years earlier in Hay River.
Worden was shot four times as he was chasing Bulatci, who had come to Hay River to sell drugs.
He was sentenced to life in prison with no chance of parole for 25 years.
His appeal documents, filed a month after his conviction, challenged more than a dozen rulings made by the original trial judge.
One of those rulings by Justice John Vertes allowed intercepted jailhouse conversations to be presented to the jury as evidence. The documents said that violated Bulatci's charter rights.
During the trial, court heard excerpts of several taped conversations Bulatci had with his girlfriend and father in which he asked them to approach a witness — a cab driver who saw Bulatci run from Worden and then heard gun shots.
Bulatci is appealing, even though he admitted during his trial to shooting the RCMP officer. But he also said he never intended to kill him. He told jurors he shot at Worden's legs and the last two shots went off accidentally while the two men scuffled on the ground.
Bulatchi cannot be acquitted because he admitted in court to shooting Worden.
(APTN, The Canadian Press)