"Attempts were made, by calling to him, to encourage him to come in."
Ms van Uden said the fully clothed man was splashing and it was thought he was responding to the calls, but then he turned and was heading away from the beach.
He was seen to be struggling and submerging 30m to 40m from the shore, she said.
"Const Redaelli disrobed, jumped into the water and swam out to him. The swimmer was unco-operative, hindering the constable's attempt to help him."
Water temperature in the lake was between 8degC and 10degC - hypothermic conditions.
Air temperature was sub-zero and an ambulance was called to await their arrival on the beach.
"Const Redaelli assisted the man ashore, where he was attended to by bystanders and ambulance staff," Ms van Uden said.
"Aaron Redaelli was coughing up water and shivering uncontrollably. He was taken by colleagues back to the police station to shower and warm up."
The swimmer was treated for hypothermia in hospital. He was referred to mental health services the next day.
Const Redaelli told the Otago Daily Times the medal was "a lovely honour" and a good story for the police in general. His partner and daughter, who attended the ceremony, as well as his family in the North Island, were "quite proud," he said.
"I remember it was cold. There wasn't much conscious thought about what was going on in my decision to go in the water, it was more 'Someone's going to have to do something with this guy', because he was starting to stay under for longer and longer," he said.
"Once I got out there and had a little bit of an issue getting him to come back in and then half-way back in, that's when the cold really hit. My arms and legs weren't feeling too flash and I remember being exhausted when I got back.
"I gave him one last push and someone grabbed him and I just sat in the water on the side there, because I just couldn't stand up. It was almost though I couldn't feel my arms and legs."
The officer of six years, all served in Queenstown, was pleased the police as a whole had been recognised.
Senior Sergeant John Fookes, of Queenstown, said it was "very pleasing" to see Const Redaelli recognised for action which was thoroughly deserving of reward.