Bends in roads can cause crashes but a recent study in the UK found that areas with mostly curved roads had lower crash rates than areas with straighter roads. This present study aimed to replicate the previous research in a different country. Variations in the number of fatal road crashes occurring between 1996 and 2005 in 73 territorial local authorities across New Zealand were modelled against possible predictors. The predictors were traffic flow, population counts and characteristics, car use, socio-economic deprivation, climate, altitude and road characteristics including four measures of average road curvature. The best predictors of the number of fatal crashes on urban roads, rural state highways and other rural roads were traffic flow, speed limitation and socio-economic deprivation. Holding significant factors constant, there was no evidence that TLAs with the most curved roads had more crashes than elsewhere. Fatal crashes on urban roads were significantly and negatively related to two measures of road curvature: the ratio of road length to straight distance and the cumulative angle turned per kilometre. Weaker negative associations on rural state highways could have occurred by chance. These results offer limited support to the suggestion that frequently occurring road bends might be protective.