We aimed to search whether neurological symptoms or signs (NSS) and the MEWS (Modified Early Warning Score) score were associated with in-hospital mortality or oxygen requirement during the first 14 days of hospitalization in COVID-19 patients recruited at the University Hospital in Krakow, Poland. The detailed clinical questionnaires on twenty NSS were either filled out by patients prospectively or retrospectively assessed by neurologists based on daily medical records. NSS were considered high or low-risk if they were associated with increased or decreased mortality in the univariable analysis. This cohort study included 349 patients with COVID-19 (median age 64, interquartile range (51–77), women 54.72%). The presence of high-risk NSS (decreased level of consciousness, delirium, seizures, and symptoms of stroke or transient ischemic attack) or its combination with the absence of low-risk NSS (headache, dizziness, decreased mood, and fatigue) increased the risk of in-hospital mortality in SARS-CoV-2 infection 3.13 and 7.67-fold, respectively. The presence of low-risk NSS decreased the risk of in-hospital mortality in COVID-19 patients more than 6-fold. Death in patients with SARS-CoV-2 infection, apart from NSS, was predicted by older age, neoplasm, and higher MEWS scores on admission. High-risk NSS or their combination with the absence of low-risk NSS increased the risk of oxygen requirement during hospitalization in COVID-19 patients 4.48 and 1.86-fold, respectively. Independent predictors of oxygen therapy during hospitalization in patients with SARS-CoV-2 infection were also older age, male sex, neoplasm, and higher MEWS score on admission.