Daniel Boulton, 30, was seen at Hallington House Farm, near Louth, just before midday on June 1.
A jury at Lincoln Crown Court heard Boulton had run away from PC Stephen Dennis who had tried to detain him while walking his dog near Hubbards Hill in Louth.
Boulton had spent the night in a nearby cottage after brutally stabbing to death his former partner Bethany Vincent, and her nine-year-old son Darren Henson, it is alleged.
The jury heard farm manager Greta Roberts was driving through the property when she noticed a man with a blue rope around his neck run out from the side of the silage store.
Mrs Roberts said she realised the man was probably the suspect wanted by police and instinctively locked her vehicle as he came towards her car and tried the door handle.
“I put my foot down and drove away,” Mrs Roberts said in her statement which was read out in court.
The jury heard Boulton encouraged armed officers who arrived at the scene to shoot him but he was tasered and held on the ground.
A silver kitchen knife was taken from him, and he was also found to have two skateboard type pads on his knees.
Boulton made no comment when he was arrested on suspicion of the two murders and assaulting PC Dennis.
The court heard Boulton was transported to Skegness Police Station and taken into custody where he made several comments to an officer observing him.
Boulton asked the officer: “Does this happen often, when people kill their girlfriend?”
He also told the officer he had a baby.
Boulton, 30, of Alexandra Road, Skegness, admits the manslaughter of his former girlfriend Bethany Vincent and her nine-year-old Darren Henson, but denies their murder.
Ms Vincent and Darren, known to his family as DJ, were both found stabbed to death at their home in High Holme Road, Louth, shortly after 8pm on May 31 last year.
• The trial continues.