He cautioned the jury against being moved by sympathy or prejudice - of being moved by their hearts rather than their heads.
There were four matters the Crown needed to prove, he said.
There are four charges relating to the two complainants - one of whom is a victim of a separate domestic assault, a case which Burke worked on.
That complainant, whose name is suppressed by law, alleges Burke came into her room, undressed, and rubbed himself against her on a bed.
She also alleges Burke pinned her against a wall to grope her and press against her.
On a third occasion, she alleges he exposed himself then forcibly performed oral sex on her.
She later moved overseas and in 2017 made a formal complaint about Burke's alleged crimes.
Burke later gave recorded police interviews telling officers that his contact with her was limited.
"We are a busy office," Burke said.
He also denied claims he brought her gifts of any kind or that he asked a flatmate how to win her over.
"That is totally incorrect," he said.
"And 'how would I win her heart?' – it's not language I would use."
As he was interviewed, police asked him to describe his physical appearance at the time.
Burke said he had a moustache then and probably weighed a few less pounds.
But he did not have a tattoo as the complainant claimed and he took off his shirt to prove it to the officers present.
The court heard, the same woman had later emailed him to enquire about the clean slate legislation and Burke had informed her of how to sign up for the victim notification register.
"How did that relationship end and why are we sitting here now?", the police interviewer asked Burke.
"As you see she has had contact with me right up until 2014," Burke said.
"I'm at a loss to explain it to be perfectly honest. I don't know what the motivation is behind it. I haven't got a clue."
The other complainant came forward in 2017 and again Burke then underwent a recorded police interview - this time telling police their sexual contact was consensual.
He said he understood that she had been spurned by a fraudster he was investigating.
They had struck up a friendship, he said.
"[We] caught up for coffee and bits and pieces. I think she may have contacted me when she found out he was arrested."
Burke said she invited him out for dinner before inviting him for dinner at her home.
At the end of the evening she showed him the spare room for him to stay, he said.
But he told police she later came into the room again to join him and this was consensual.
Burke was suspended from police work in April 2017 when a criminal investigation, led by detectives based in Christchurch, began.
Burke began giving evidence today telling the jury he first joined police in January 1975 as a cadet, graduating the following year to begin working at Auckland central.
"In 1982, I took leave without pay and went farming."
In 1996, he rejoined the police as he had taken an accelerated course to graduate in November that year.
Burke said in his role it was expected that he could talk to anyone and everyone.
In about 2008 a new policy came in, part of that was a code of conduct about various behaviour - this changed common police practise and police no longer spoke to women on their own.
It was safeguard not only for police but for victims and witnesses, he said.
Burke will continue to give evidence tomorrow.
