The bullet went through the 52-year-old's left arm and lung, striking his heart.
Smith called an ambulance but Taylor died before help could arrive.
Senior Sergeant Christopher Goldsmith arrived at the Henderson police station that morning shortly before Smith.
As the clock neared 5am, he introduced himself to her, escorted her to an interview room and read out her rights.
"I said you have the right to remain silent," he told the court today.
"You do not have to make any statement. Anything you do say will be recorded, may be given in evidence in court.
"You have the right to speak with a lawyer without delay and in private before deciding whether to answer any questions.
"Police have a list of lawyers you may speak to for free. Do you understand your rights?"
Crown prosecutor Emma Smith asked what the defendant's response was.
"She said: 'Yeah sweet. I just shot him. I didn't know it was him'."
The senior sergeant then told the defendant about the next steps, how a female colleague would take swabs of her hands and photos.
Amy Christine Smith in the High Court at Auckland on the first day of her trial. Photo / Chelsea Boyle "She said: 'Yeah sweet. I will tell you everything. I thought he was an intruder and I shot him'."
Smith then wanted to speak to her aunt - a lawyer - and police began making attempts to contact the aunt, including leaving a voicemail.
Smith was asked if there was anyone else she wanted to speak to, the court heard.
The court heard she replied: "I don't know what the f**k to do. I shot him."
Several more attempts were made to rouse another lawyer for her and by 6.30am she was able to speak to a lawyer on the phone.
When Goldsmith re-entered the room, he asked if she would be making a statement.
"My lawyer told me not to say anything.
"All I know is that my partner is not here because of me.
"I am a total f**k up. Everything is frazzled in my head.
"And I don't want to say anything because I don't know what is true and what is not."
About 8.30am she was also able to speak to her aunt on the phone.
When in the presence of two lawyers, including her aunt, Goldsmith told Smith she was being formally charged with murder.
Last week, the jury heard from the first police officers to arrive at the crime scene.
Sergeant Simon Brown co-ordinated the initial response on the ground as they descended on foot, leaving their cars parked about 400m away.
"There was no street lighting whatsoever," he said.
The sky overhead was clear enough to see stars but it was a dark area, he told the court.
"Walking on that gravel road, you couldn't see if there was a pothole in front of you."
Police launched a homicide investigation after they were first called to the rural address in South Head about 2am. Photo / Dean Purcell The barn, however, was well lit, he said.
As officers secured the barn Brown noticed the "pungent" smell of cannabis on the upper level.
Cannabis bundles hung from the ceiling there like a "dried florist arrangement".
It was deemed safe for the ambulance staff to enter and Smith was taken outside.
She was obviously upset - hysterical, angry and crying, Brown said.
"I do recall her saying: 'I don't want you here. I want the ambulance here.' Something along those lines."
Brown noted she lashed out at one of the officers, he said.
The jury trial, presided over by Justice Mary Peters, continues in the High Court at Auckland.