The short answer is "yes." There are no standards, rules, or regulations that per se prevent a NP from discharging a patient. However in no case should you discharge a patient if that would result in the threat of serious harm or actual harm or danger to the patient because there is no alternative health care provider available.
NPs, like other heath care professionals are expected to act in a manner consistent with their professional responsibilities and standards of practice. If a NP believes that he/she is unable to manage the medical and nursing issues of a patient, the duty of care would require that the patient be discharged. Reasons for being "unable to manage" could include patient noncompliance, an "uncomfortable fit," or lack of resources to provide proper treatment.
If you are required to discharge a patient, it is important to document both the reasons why and that there has been communication between you and the patient (or guardian) regarding the termination of services. Included in that communication should be a referral to other health care services and/or practitioners to resources that can provide the necessary information for continued treatment. Any referral information provided to the patient that can be reproduced should be placed in the patient's chart along with your notes.