In a hospital place of service, CMS does allow a split or shared service to be billed under the physician, but only if the physician has performed and documented a "face-to-face portion" of the E&M service. Per Chapter 12 of the Medicare Claims Processing Manual:
When a hospital inpatient/hospital outpatient (on campus-outpatient hospital or off campus outpatient hospital) or emergency department E/M is shared between a physician and an NPP from the same group practice and the physician provides any face-to-face portion of the E/M encounter with the patient, the service may be billed under either the physician's or the NPP's UPIN/PIN number. However, if there was no face-to-face encounter between the patient and the physician (e.g., even if the physician participated in the service by only reviewing the patient’s medical record) then the service may only be billed under the NPP's UPIN/PIN.
'Signing off' on a note is not sufficient by itself to allow the service to be billed under the physician's credentials - if the physician isn't seeing the patient, then it would have to be billed under the NP.
I an office setting, the 'incident to' rules would apply, and since a consultation is an evaluation for a new problem, it would not meet the definition of 'incident to' and would have to be billed under the NP as well.
