The force said officers were working to establish the vehicle involved and have appealed for anyone who might have relative CCTV footage to contact them.
“If you were driving the vehicle westbound on the B6265 between 1.44am and 3.10am on Sunday, please do the right thing and contact the police.
“If you know or believe you may know who was behind the wheel due to damage seen on a vehicle, make a report without delay.”
Tributes have also been paid by his employers at the Royal Oak pub in Pateley Bridge.
Owner Robert Jackson, who had known Mr Chadwick all his life as he was friends with his parents, described him as a “true gentleman”.
“He was a fantastic person,” he said.
“A fine young man who was polite, helpful and the best barman.
“We all miss him so much. It is such a waste as he had his whole life ahead of him.”
A post on the pub’s Facebook page said the team’s “thoughts are with his family and friends at this time”.
“I would ask everyone to bear with us a little bit as there’s a rather large hole to fill both personally and professionally for each and every one of our team,” it said.