Road spikes were deployed and the vehicle was located abandoned on Chadwick Place.
A firearm was also located on the road where the vehicle had travelled.
Police and police dogs searched the area and were eventually led to an address nearby where a man was taken into custody.
An incident on Sunday morning involved police following two vehicles before one turned and drove back towards the police vehicle.
An officer heard what they thought was a firearm being discharged and a bullet hole was later confirmed to be in the front of the police car.
It is believed these two incidents are linked.
Police in Levin are currently managing gang-related tensions under powers granted by a Gang Conflict Warrant and their counterparts in Palmerston North are considering applying for similar controls.
“I’m pleased we have arrested someone in relation to this morning’s offending and locking someone up for that is a huge relief and a testament to the solid work of police staff across Manawatū,” said Central District Commander Superintendent Dion Bennett.
“We will be relentless in our pursuit of safety – for our staff, our communities and all who live in them.”
The arrested man was expected to appear in Palmerston North District Court today on one charge of using a firearm against a law enforcement officer and on a warrant for outstanding driving offences.