PC Paul Tincello was due to appear before a misconduct hearing this week but the officer resigned days before it started.
It is alleged that PC Tincello had attended the crash in July in Tunbridge Wells last year.
It is alleged he failed to arrest a driver after taking a reading of 65mg of alcohol per 100ml of breath. The legal limit is 35mg.
Simon Walsh, acting on behalf of Kent Police, told the panel PC Tincello avoided the arrest as he needed to finish on time on the night in question.
The driver was later breathalysed in hospital by another officer and arrested for the offence.
As PC Tincello failed to attend the hearing, despite still being an employee of Kent Police until his notice period ends on July 18, the hearing had to be adjourned.
While the resigning officer had sent in a statement, along with questions to be asked of witnesses to the Kent Police Federation, they informed the panel that in was not ‘appropriate’ for them to cross examine fellow officers.
Chairing the panel at the misconduct hearing, Claire Harrington said: “It’s incredibly frustrating. We’re half a day into a hearing and have made no substantial progress at all.”