Dayton police rushed to the scene shortly after 7 p.m. (2300 GMT) but the suspect had fled the scene.
All occupants were taken to local hospitals and at least three of them were in life-threatening condition when they were transported, Lt. Eric Henderson said.
The incident unfolded when Walters' father was trying to take his son to a hospital for mental health issues, but when the suspect realized where they were going, he began assaulting his father, Biehl said.
Two officers also sustained minor injuries when the suspect struck their vehicle, as did the suspect.
Video from the scene by NBC affiliate WDTN of Dayton showed a heavily damaged police vehicle with the front and rear smashed in.
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Police responded to a stabbing complaint in OH only to find out the suspect had fled.
Soon after driving off, Walters crashed in the neighboring suburb of Riverside and then he jumped into a Riverside police SUV that had responded to the crash, police said. Police confirming early Tuesday morning, the two dead are among the seven kids reported injured in the accident. There were three adults in the SUV, the police said.
Police say the family in the minivan had just visited the city's downtown library Monday night when Walters slammed into them.
He managed to climb into the driver's seat of the police cruiser. His name was not immediately released.
The impact split the stolen cruiser into several large pieces.
"I jumped out and did my best to get as many children out of the van as I could", he told WHIO-TV.