Burke and Mr Fyfe began pursuing the deer on foot in a manuka stand about 40 x 50m in diameter, both with rifles.
Sgt Collin said Burke thought Mr Fyfe was behind him, however Mr Fyfe had headed into the middle of the manuka, walking away from and slightly parallel to his friend.
"The defendant could no longer see the deer but could hear movement in the manuka. He stated he briefly saw sighted the legs of the deer in the light from his head torch, moved further around the stand . . . to a small clearing and could again hear movement.
"He stated he saw 'a small eye reflection, about 60m away . . . that was moving away' . . . [and] described it as a 'silver blue colour which was just like a deer eye reflection'."
After calling out to Mr Fyfe, Burke aimed through his scope, fired one round at the reflection, thinking he'd shot the deer.
He again shouted to Mr Fyfe and got no reply.
"The defendant went to the area . . . and saw the deceased lying on the ground."
Sgt Collin said Mr Fyfe showed no outward signs of life and when Burke moved him into the recovery position he saw the bullet hole in the back of his head.
Judge Kevin Phillips remanded Burke on bail to 9.30am on May 14 for sentencing, ordering a pre-sentence report to include an emotional harm reparation report, detailed and updated victim impact statements and options for community and home detention sentences, although he warned it was no indication of the sentence.
The maximum penalty for the charge is three years imprisonment or a $4000 fine.