One of the predominant symptoms of the COVID-19 virus is the complete (anosmia) or partial (hyposmia) loss of smell. Anosmia may be a critical neurocognitive symptom because there is an empirically demonstrated association of anosmia with neurodegenerative diseases like Parkinson's disease, Alzheimer's disease, etc. The present study assessed the neurocognitive disorder patterns in recovered COVID-19 patients who either self-reported anosmia or its absence. Of the 60 adult participants (n = 32 males, n = 28 females; Mage = 20.78 years, range = 18–31 years), 15 reported COVID-19 induced anosmia, 15 reported COVID-19 without anosmia, and 30 reported not having contracted COVID-19. The participants were first administered a 10-item smell test, and analysis of variance revealed significantly better scores for the control group than the other two groups. Further, there was no significant difference in smell scores between the patients who self-reported anosmia or denied it. This statistical pattern was consistent across all neuropsychological tests: short- and long-term verbal memory, digit span, Trail Making, and a self-report 46-item neurocognitive scale. Regardless of the self-report of anosmia or denial, all thirty COVID-19 patients scored significantly poorer than the control group on all of the tests and neurocognitive scale. In summary, the self-report of anosmia appears to be unreliable, and the COVID-19 patients who were found to be anosmic on the initial objective smell test demonstrated poorer neuropsychological performance than controls.