During the first wave of infections, neurological symptoms in Coronavirus Disease 2019 (COVID-19) patients raised particular concern, suggesting that, in a subset of patients, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) could invade and damage cells of the central nervous system (CNS). Indeed, up to date several in vitro and in vivo studies have shown the ability of SARS-CoV-2 to reach the CNS. Both viral and/or host related features could explain why this occurs only in certain individuals and not in all the infected population. The aim of the present study was to evaluate if onset of neurological manifestations in COVID-19 patients was related to specific viral genomic signatures. To this end, viral genome was extracted directly from nasopharyngeal swabs of selected SARS-CoV-2 positive patients presenting a spectrum of neurological symptoms related to COVID-19, ranging from anosmia/ageusia to more severe symptoms. By adopting a whole genome sequences approach, here we describe a panel of known as well as unknown mutations detected in the analyzed SARS-CoV-2 genomes. While some of the found mutations were already associated with an improved viral fitness, no common signatures were detected when comparing viral sequences belonging to specific groups of patients. In conclusion, our data support the notion that COVID-19 neurological manifestations are mainly linked to patient-specific features more than to virus genomic peculiarities.