Background Intellectual disability (ID) is associated with violent and sexual offending and victimization, but the importance of neuropsychiatric comorbidity and severity of disability remains unclear. Methods In a register-based cohort study of people born in Sweden 1980-1991 (n = 1 232 564), we investigated associations of mild and moderate/severe ID with any, violent and sexual crimes, and with assault victimization, stratified by comorbid autism and attention deficit hyperactivity disorder (ADHD). We defined ID by attendance at a special school or registered diagnosis and obtained data on criminal convictions and injuries or deaths due to assaults from nationwide registers until end of 2013. Results Compared to people without ID, autism or ADHD, men and women with mild or moderate/severe ID and comorbid ADHD had elevated risks of violent crimes [range of hazard ratios (HRs) 4.4-10.4] and assault victimization (HRs 2.0-7.7). Women with mild ID without comorbidities or with comorbid autism also had elevated risks of violent crimes and victimization (HRs 1.8-4.6) compared to women without ID, autism or ADHD. The relative risks of sexual offending and victimization were elevated in men and women with ID without comorbidities (HRs 2.6-12.7). The highest risks for sexual offending in men (HRs 9.4-11.0) and for sexual assault victimization in women (HRs 11.0-17.1) related to ID and comorbid ADHD. Conclusions The elevated risk of violent offending and assault victimization in people with ID is largely explained by comorbid ADHD, whereas ID is independently associated with sexual crimes and victimization, even though absolute risks are low. Copyright © The Author(s), 2022. Published by Cambridge University Press.