Lincolnshire Police have appealed for any witnesses to the 10-mile trip the 29-year-old took on Monday from Saltfleetby to Louth.
Boulton was arrested on Tuesday following a 15-hour manhunt after his 26-year-old ex-partner Bethany Vincent and her son Darren Henson were stabbed to death in High Holme Road, Louth, at around 8.29pm the previous day.
The suspect was arrested in bare feet at around midday at a farm near Louth, after a man banged on a neighbour’s car window shouting “let me in, let me in”.
Police said Boulton remains in custody.
Detective Inspector Andy McWatt, from the East Midlands Special Operations Unit, said: “Daniel Boulton may have got a lift from Saltfleetby to Louth on May 31.
“If you have information relating to this, please get in touch.
“Our investigation continues at a pace, and even a sighting or any piece of information – however small you think it may be – could prove vital.”
The force said both victims had suffered multiple stab wounds at an “absolutely devastating and dramatic scene”, and a knife believed to have been used to inflict the injuries was recovered.
An off-duty Lincolnshire Police officer was also injured in the Hubbard’s Hill area of Louth on Tuesday morning amid the manhunt for Boulton.
A neighbour at the scene of where a man was arrested in connection with the double stabbing told the PA news agency she managed to escape after he banged on her car window.
The woman, who asked not to be named, said after the man attempted to get into her car, she drove down the road to where she had seen police vehicles in nearby Hubbard’s Hills.
Forensic officers also appeared at the scene of the arrest around four hours later.
Armed officers and several police vehicles were involved in the arrest at the farm in Hallington, near Louth.
Two officers in high-vis jackets escorted a man into a police van around the back of a farm building.
He was wearing no shoes or socks, ripped tracksuit bottoms, an Adidas T-shirt and a Nike jacket.
An air ambulance and a number of police vehicles could be seen in the Hubbard’s Hill area where a police officer was injured.
Police said no-one else was injured at the property where the stabbing happened, but another young child was found there and they have since been safeguarded.