Final answer:
The nurse would have broken the Health Insurance Portability and Accountability Act (HIPAA) by allowing a family member to speak to a patient without proper consent or authorization, which could lead to a violation of privacy rights.
Step-by-step explanation:
The specific law that a nurse would have broken by improperly connecting a family member to speak to a patient admitted to the psychiatric unit without proper consent or authorization is the Health Insurance Portability and Accountability Act (HIPAA). Passed in 1996, HIPAA requires healthcare providers to maintain strict confidentiality of patient records. Disclosing any private information, such as allowing a brother to speak to his sister without her consent, could potentially lead to a violation of the patient's privacy rights under this act.