Inpatient Opioid Safety Act of 2021 This bill requires hospitals, as a condition of Medicare and Medicaid participation, to use specified technology to monitor patients for opioid-induced respiratory depression for 12 hours after the administration of an opioid or until the patient is discharged, whichever is earlier, unless a health care practitioner determines before administering an opioid that such monitoring should not be used and records this determination in the patient's record.