At least two shots were fired at a New Plymouth house and vehicle in its driveway at around 4.30am on Sunday, police say.
No one was injured in the drive-by shooting, detective senior sergeant Drew Bennett said.
It was not believed to be a random incident or gang-related, he said.
Police were now appealing for any sightings of a two-door yellow Audi TT between 2.30am and 4am in the New Plymouth, Bell Block and Waitara areas.
"We are also asking for any residents in the Bell Block area around Penrod Drive, Wills Road and Mangati Road who have heard or seen the shooting and, importantly, anyone with private CCTV to contact police urgently.
"We are following a number of lines of enquiry and want to assure the public we are treating this matter extremely seriously."
Anyone with information about the incident can ring 105 or visit their local police station, quoting file number 230319/1164.
Information can also be provided anonymously via Crime Stoppers on 0800 555 111.