By law, how often do air conditioning units in offices need to be serviced?

Unless your state has a law, and I don't know of any that do, the mechanical system maintenance it left to the discretion of the building owner. I work on large commercial buildings and we clean and service room type air conditioners once a year and service and change filters in large, central units twice a year.

I don't know of any law requirement for AC service. Once installed, there's a warranty period, but no requirement for service. Most technicians recommend at least an annual check, but there's no requirement that says it has to be done. And unless you paid for some kind of service contract with the installer, they won't come back to service it unless you tell them to. Service is at the expense of the owner of the AC unit or renter, not the installer, unless it is warranty repair work.

You may not have a law covering something like that. Outside of replacing the filter(s) if the units have any, and that is as needed or recommended, the only time our building units are serviced is when they break. But it could be some communities do have a law covering this.
So:
1. Check you local city code,
2. Ask your city building inspector or
3. OSHA.

On the other hand, if there are special health needs involved based on environment you may want to ask your employer to check with building maintenence or the landlord.