Surgery is not typically billed as an RHC encounter. Instead, it falls under the CAH's outpatient billing procedures. RHCs are designed for primary care services. Surgical procedures, especially those requiring hospital resources, generally fall outside this scope.
Services that qualify as RHC services are billed by the RHC under its own billing procedures, even if the service is provided within the physical location of a CAH. Conversely, services that do not meet the definition of an RHC service should be billed under the CAH's or the individual provider's billing methods.
If you need additional information, I have attached some resources below with the most accurate and up-to-date information on how the professional service of a surgery performed by an RHC provider.
Critical Access Hospitals: Bill Correctly
Noridian Medicare Critical Access Hospitals: Bill Correctly