The answer is maybe--
References (2009 IBC)
907.2.6.1.1 and 907.2.11.2 and exception 2-- require either system or single station smoke detectors in I-1 patient rooms
407.7, 907.2.6.2 require smoke detectors in either the corridor, the patient rooms or the door between them for I-2 nursing and detox facilities.
I-2 acute care facilities do not require smoke detectors in patient rooms due to the presumed presence of staff and the presumed inability of the patients to self evacuate.
2006 NFPA 101 A.18.3.4.2, A 19.3.4.2 "It is not the intent of this code to require single staiton smoke detectors that might be required by local codes to be connected to or to initiate the building fire alarm system."
Has similar language regarding nusring homes fo reither corridors or patient rooms or the door between them.
Note that other local regulations may be different.