Two other people who were in the vehicle were detained for questioning by the Ohio Bureau of Criminal Investigation, the chief said, which is taking over the investigation.
A spokesman for BCI confirmed that it is investigating the shooting, but declined further comment.
Daulton said New Lebanon police have turned over all information to BCI, including body camera footage that the officer was wearing at the time of the shooting.
The incident was initially reported as a traffic stop around 12:30 a.m. Law enforcement officials were on the scene for several hours, but by late morning the scene was cleared.
The shooting was the second officer-involved shooting in Montgomery County this week. The first took place in Dayton Sunday night, where three officers opened fire on Donald Saunders, striking him at least four times and eventually killing him.
Police said Saunders pointed a gun into the chest of the supervising officer before the shooting took place.
Dayton Police Professional Standards Bureau is investigating that shooting.