The car crashed into a CityRide bus that had six passengers inside on the corner of Ranolf and Amohau Sts before carrying on and then crashing into a tree on Pretoria St, police said.
The occupants of the car ran off and police were still trying to find them.
A police media spokesperson said police had reports a similar vehicle was reportedly firing a BB gun or similar from the windows of the vehicle on Shirley St, Mangakakahi.
A witness who lives on Shirley St told the Rotorua Daily Post she saw a vehicle fitting the same description firing shots at school children on the side of the road.
Earlier today Rotorua police crime prevention manager Inspector Stuart Nightingale told the Rotorua Daily Post Mazda Demios were being targeted by a group of youngsters trying to steal them.
Two Mazda Demios were stolen from Rotorua at the weekend and two others were interfered with.
Mr Nightingale said it followed a trend police were seeing in Tauranga and Hamilton where thieves were targeting a specific make of car.
"Once they learn how to break into a particular make and model they stick with them.
"They go for what's easier to steal because they are lazy by nature."
Mr Nightingale said sadly young people were often involved when it came to stealing cars and being chased by police.
"It all seems like a bit of fun to them before someone gets hurt or killed."
A yellow 2002 Mazda Demio registered EGK430 was taken from Hinemoa St during the day on Sunday and a blue 1998 Mazda Demio registration HMY862 was taken from Mount View Dr in Mangakakahi overnight on Sunday.
Three other Mazda Demios have been broken into since Thursday last week.
A 2000 white Mazda Bounty double cab ute registered zd9807 was taken from Kingsley Rd in Ngongotaha overnight on Saturday.
Meanwhile, two other vehicles were also broken into at the weekend in the Victoria suburb, one on Eason St and the other Herewini St.
Mr Nightingale said on one of those occasions offenders were disturbed with witnesses saying those responsible looked between 10 and 12 years old.