Beau Lamarre-Condon has pleaded not guilty to murdering his ex partner Jesse Baird and Luke Davies in their inner-city terrace on February 19, 2024.
Police tried unsuccessfully to contact him for four days before he turned himself in.
He then led officers to a rural property where the bodies of both men, who were aged in their 20s, were found in surfboard bags.
"I just either want to let a detective or a sergeant know I am not avoiding them," the 31-year-old said during a three-minute phone call to police on February 22.
"Just tell them I will come in tomorrow."
This evidence was heard during a NSW Supreme Court jury trial on Thursday as prosecutors read a statement by the officer who took the call, Constable Kye Richards.
The morning before the alleged murders, Lamarre-Condon messaged a friend - known by pseudonym Fiona Rosso - not to worry about him and that he would call later.
"Also I've just gotten rid of all social media," he wrote.
He turned up to Ms Rosso's home three days after the alleged murders crying and saying he had "done something bad", the jury heard on Wednesday.
Lamarre-Condon told her police had tried to contact him but he put his phone on aeroplane mode.
Armed with two buckets, he scrubbed blood from the back of a white van parked outside Ms Rosso's home, the jury heard.
He then spent the night there before driving to Sydney.
Ms Rosso testified Lamarre-Condon's mother texted him the code word "hot chocolate", meaning police had searched her home after the alleged murders.
A statement by Constable Hayley Keefe was read on Thursday outlining attempts by NSW Police to contact her colleague and friend.
She was asked by a crime manager to contact Lamarre-Condon on his personal Instagram account.
On February 21, she followed through.
"Hey hun ... can you please contact the crime manager at eastern suburbs asap when you get a chance?" she wrote.
The message remained unread and she deleted it, feeling awkward for using her personal social media for business, she wrote in her statement.
The Crown alleges Lamarre-Condon killed Mr Baird "execution-style" at close range through a plan borne of a jealous obsession, before shooting Mr Davies to eliminate a witness.
The 31-year-old claims he killed the men in self-defence after entering their terrace to retrieve his belongings.
His offer to plead guilty to Mr Baird's manslaughter was rejected by prosecutors.
The trial continues.
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