Yes, you can code both as long as it doesn't conflict with your specific contract guidelines. See AHA Coding Clinic 4th quarter 2013 (Volume 30 Issue 4) - Admission for Rehabilitation... question 4.
Question 4:
The patient was transferred to a skilled nursing facility’s rehabilitation unit for occupational therapy and physical therapy, following a prolonged stay at a long term care hospital (LTCH), where she was successfully weaned off mechanical ventilation. At the SNF, the patient received rehab due to deconditioning and debility. The provider documented that the patient presented with complex medical problems (i.e.,
chronic hypoxic respiratory failure, requiring supplemental oxygen,
chronic obstructive pulmonary disease (COPD), tracheostomy status, type II diabetic neuropathy, and obesity). What are the appropriate code assignments for the rehabilitation stay at the SNF?
Answer:
Assign code
J96.11, Chronic respiratory failure with hypoxia, as the principal diagnosis. In this case, the underlying reason for the debility and deconditioning is coded as the principal diagnosis.
Assign also codes
J44.9, Chronic obstructive pulmonary disease, unspecified;
E11.40, Type 2 diabetes mellitus with diabetic neuropathy, unspecified;
E66.9, Obesity unspecified;
Z99.81, Dependence on supplemental oxygen; and
Z93.0, Tracheostomy status.
COPD is common cause of respiratory failure.
Hope this helps