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The presence of asymmetric information is an important source of efficiency loss for insurance companies and could reduce profitability. In this paper, we test the conditional independence of coverage choice and risk, where “conditional” means conditional on all variables observed by the insurer. We use two parametric a pair of probits and a bivariate probit model. The data includes all third-party and hull policies as well as claims data for private automobiles during 2013-2016. The data are derived from the administrative database of a small insurance company in Iran. Once we control for individuals’ risk aversion by limiting our test to subsamples of individuals who only bought minimum third-party insurance, we find evidence for the presence of asymmetric information. Based on our results, those who bought hull and third party insurance have higher risk of accident in comparison to those who only bought third party insurance. The existing premiums does not fully compensate for this extra risk.