Off-duty police officer shoplifts a pair of sunglasses. Your opinion?

For three years, I sat on the Disciplinary Board of my police department. It was an honor to be asked and to serve. After an internal police investigation of suspected bad conduct, many officers were faced with the Disciplinary Board and yours truly. One case has always stood out in my mind. An off-duty officer walked into a store, cutoff the price tag, and walked out the front door, without paying for a pair of sunglasses. After hearing the details of this case, I could not believe that an officer would resort to a petty crime and placed his job and pension in danger. We also learned that this same officer had gone into a grocery store, opened a jar of mayonaise, stuck his finger inside just to see if he liked the taste of it. This case had not come before the Disciplinary Board, so we tied the two cases together. I knew this officer quite well and his actions totally surprised me. Since I was the only police officer on the board, the other members relied heavily on my decisions. My suggestion to the board was to terminate this man for “conduct unbecoming a police officer”. The entire board agreed with my decision and he was terminated.
Question: was just terminating this officer enough? Should he have been arrested?