This is extremely agency specific and a general answer cannot be given. It can also vary with the administration.
During the years I was active, both a street officer and in our training division (as a training officer, not trainee), duty firearms were department issue as was duty ammunition. Training/qualification ammunition was department issue for department weapons. If you chose to carry a personal weapon, either on or off duty, you had to be certified with it and provide your own ammunition to qualify. Ammunition for a personal weapon could be provided by the officer or department, if the gun used a caliber the department owned guns for, or provided by the officer. Personally provided ammunition had to be factory and meet department requirements.
For qualification the department provided the ammunition, which was generally commercially reloaded and of varying quality. For personal weapons the individual could use whatever he chose that was appropriate for the weapon.