What FAA document specifies the accuracy to which an airspeed indicator must be calibrated to?
There are two standards, one for traditional pitot/static devices and one for air data computers.
Traditional A/S indicators are covered by TSO-C2d which references Society of Automotive Engineers, Inc., (SAE) Aerospace Standard (AS) 8019, "Airspeed Instruments", dated March 30, 1981.
Air data computers are covered by TSO-C106 which references SAE AS 8002, “Air Data Computer - Minimum Performance Standard,” dated October 30, 1981.
The SAE documents must be purchased.
Accuracy in the AS docs is not stated as a simple value. And as the system depends on installation, the aircraft level standards are applicable.
For traditional A/S indicators, repeatability is more important as installation can add errors. The aircraft manufacturer typically provides an IAS to CAS table in the POH. Since Part 23 aircraft rules have moved to a functional standard (e.g., it has to do its job well enough to be safe), there's no specified accuracy.
For Part 25 aircraft where air data computers are the norm, they must meet 14 CFR §25.1323 Airspeed indicating system.