Helping Account for Rural Medical Outpatient Needs in Oklahoma Act or the HARMON Oklahoma Act This bill requires the Centers for Medicare & Medicaid Services (CMS) to continue to allow Harmon Memorial Hospital in Hollis, Oklahoma, to retain its designation as a critical access hospital and to seek designation as a rural emergency hospital under Medicare after the end of the COVID-19 public health emergency, as specified in a prior letter sent to the hospital. The bill also requires the CMS to issue final regulations implementing the newly created Medicare rural emergency hospital program by November 1, 2022.