A worker at the Wheelwright Shop in Gladstone said the car zoomed past their workshop, opposite the corner at the intersection.
He was working out the front of the shop by the road when a police car stopped. The officer was about to wind down the window and talk to him but before he had the chance, the car went screaming past, toward Masterton. The policeman had to do a U-turn in pursuit, he said.
The fugitive then "flew past" Colombo Rd in Masterton, a resident said.
Mr Glassey said the chase had lasted about 20 minutes.
Five police cars responded to the call-out but only two were used to closely pursue the car.
"We only used cars to keep him clear of the urban area for the safety of others."
The rest of the cars were stationed in and around Gladstone in an attempt to stop the man without anyone getting hurt, Mr Glassey said.
The chase had ended when the man drove into Masterton, pulled the car into the Wairarapa Hospital carpark and sprinted into the main entrance of the building.
Hospital reception staff said they saw the man rush in but couldn't give any more details.
Mr Glassey said the man was eventually arrested in the hospital building, but not before giving his newborn baby a quick visit.
Police said that, when caught, the man had told police he only tried to evade them because he wanted to visit his baby.
The man had panicked when he was stopped by police, Mr Glassey said.
The car was not stolen, the man did not have a warrant out for his arrest and Mr Glassey said there was no alcohol or drugs involved or any reason to not stop for police.
"If he had just stopped, to start with, it would have just been a traffic offence."
"The reason he gave for evading police was mindless and driving like that in these conditions [raining and foggy] was mindless.
"The ultimate result is that he almost didn't get to see his newborn for the first time because of the way he drove."
The man's car has been impounded.
He faces charges of dangerous driving, speeding and failing to stop for police and is due to appear in Masterton District Court on Monday.