It happened December 15th ... a trooper with the Indiana State Police pulled the car over for following too closely. There were two men in the car -- Kohberger was driving, and the passenger presumably was his father, who accompanied him from Washington State to Pennsylvania.

Police officials say at the time of the stop they knew nothing related to the license plate or state in which the car was registered. However, more than a week before, cops asked the public's help in finding a white Hyundai Elantra -- the car in which Kohberger was driving.

Police let them go with a verbal warning. BTW, during the stop, the cop asks where they're going, and they reply, Pennsylvania ... to which the cop says, "That's a long haul. Are you guys scared of airplanes?" The cop then laughs.

During the encounter, Kohberger's dad mentions a shooting near Washington State University, adding that's where his son went to school. A man had barricaded himself in an apartment near the University and threatened to kill his 2 roommates ... he died in a police shootout.

The Indiana State Police say just minutes before that traffic stop, the 2 men were stopped by a Deputy from the Hancock County Sheriff's Dept. ... and again they were released with a verbal warning.

Kohberger was arrested 2 weeks later -- December 30th -- at his parent's home in Pennsylvania.