PC Julie Wilby started her shift at the West Yorkshire force at 7am on September 24, driving from her home three miles away.
She was required to undergo a breathalyser test at 8am that day.
The reading was 35 micrograms of alcohol per 100 millilitres of breath.
The legal limit is 35 micograms of alcohol per 100 millilitres of breath.
A previous statement on West Yorkshire Police's website said: "It is alleged that PC Wilby drove to work at a time when, on a balance of probabilities, she would have been over the legal limit to drive and that she attended work and commenced her shift when she was unfit for duty.
"It is alleged that PC Wilby has breached the Standards of Professional Behaviour in respect of Fitness for Work, Orders and Instructions and Discreditable Conduct."
A misconduct hearing, which took place at the force's headquarters in Wakefield on Monday and Tuesday this week, dismissed the allegation that PC Wilby was over the legal limit to drive, but found she attended work whilst unfit for duty.
She was given a final written warning.