Background Huntington’s disease (HD) is an inherited neurodegenerative disorder caused by an expanded CAG repeat in the HTT gene. It is diagnosed following a standardized examination of motor control and often presents with cognitive decline and psychiatric symptoms. Recent studies have detected genetic loci modifying the age at onset of motor symptoms in HD, but genetic factors influencing cognitive and psychiatric presentations are unknown. Methods We tested the hypothesis that psychiatric and cognitive symptoms in HD are influenced by the same common genetic variation as in the general population by 1) constructing polygenic risk scores from large genome-wide association studies of psychiatric and neurodegenerative disorders and of intelligence and 2) testing for correlation with the presence of psychiatric and cognitive symptoms in a large sample ( n = 5160) of patients with HD. Results Polygenic risk score for major depression was associated specifically with increased risk of depression in HD, as was schizophrenia risk score with psychosis and irritability. Cognitive impairment and apathy were associated with reduced polygenic risk score for intelligence. Conclusions Polygenic risk scores for psychiatric disorders, particularly depression and schizophrenia, are associated with increased risk of the corresponding psychiatric symptoms in HD, suggesting a common genetic liability. However, the genetic liability to cognitive impairment and apathy appears to be distinct from other psychiatric symptoms in HD. No associations were observed between HD symptoms and risk scores for other neurodegenerative disorders. These data provide a rationale for treatments effective in depression and schizophrenia to be used to treat depression and psychotic symptoms in HD.