Waikato West Area Commander Inspector Will Loughrin says there was no immediate risk to the children.
"Police are currently investigating an incident that occurred yesterday which we believe is connected to what happened this morning. We have subsequently executed a search warrant in relation to this. This investigation remains ongoing," Loughrin said.
Waikato Mayor Allan Sanson told Newstalk ZB's Heather du Plessis-Allan Drive he understood police had somebody "in hand that they were talking to".
A police spokesperson said this evening there were no updates – including regarding any arrests or people in custody.
Sanson said a man was dropping his kids off at school this morning and when another man, who was known to him, shot at his car when he was about 100m from the school.
"He hit the car three times from what I understand.
"He did have cuts they believed that were derived from the glass being shattered from the shooting."
Sanson said from his understanding no kids were at risk.
"It wasn't directly outside the school, it was 100m down the road from the school."
Sanson said this type of incident didn't happen in their community.
"You may have that happen, and it has happened, in the OK Corral of Auckland in the last couple of weeks but it certainly doesn't happen down here and that worries me that somebody thinks that's a serious option in relation to a dispute."
Loughrin said the shots were fired from the street and in view of members of the public.
Police are appealing to public for information and anyone who may have witnessed the incident.
