Harris, who was arrested Feb. 18, won't be prosecuted for those crimes due to a lack of evidence, but Seattle prosecutors are pursuing two other misdemeanors against him.
Harris, 24, whose father Capt. Phil Harris died from complications of a stroke on Feb. 9, has been formally charged with reckless driving and driving with a suspended license. If convicted, he faces a maximum of a year and three months in jail.
"We didn't file charges of DUI or hit-and-run due to insufficient evidence," Seattle prosecutor spokesman Dan Donohoe tells PEOPLE. "The witness [to the alleged crash] couldn't identify the driver."
The reality star was pulled over in his father's BMW in Seattle and was initially booked for DUI, hit-and-run and driving with a suspended license.
His next court hearing is set for March 26.