Hospitalisation with COVID-19 is associated with an increased risk of neurological sequelae; however, representative nationwide studies comparing to other infections with similar severity and also including milder SARS-CoV-2 infections have been lacking. Using the nationwide Danish registers including all SARS-CoV-2 PCR test results and hospitalisations between March 1, 2020, and December 31, 2021, we estimate the risk of any first neurological disorder diagnosed in inpatient, outpatient, or emergency room settings. We show that positive tests increase the rate of neurological disorders by a hazard ratio of 1.96 (95% confidence interval: 1.88-2.05) compared to individuals not tested and by a hazard ratio of 1.11 (95% confidence interval: 1.07-1.16) compared to individuals with negative tests only. However, there is no evidence that the risk of neurological disorders is higher for individuals who test positive compared to non-COVID-19 infections treated with anti-infective medication. The risk of neurological disorders is increased after COVID-19-hospitalisation compared to no COVID-19 hospital admission; however, these risks are comparable to hospitalisation with other respiratory infections (P value 0.328). In conclusion, COVID-19 is associated with an increased risk of neurological disorders, but no more than that observed after other infections of similar severity.