<p>Triggered by the COVID-19 crisis, one of the most severe stock market crashes in history arose in March 2020. In this study, to analyze the dynamic efficiency before and after the crash, the returns of NASDAQ insurance stock markets are utilized. The significant fluctuation clustering phenomenon is presented in the studied series during the March 2020 crash. The dynamic impacts of the March 2020 crash on the multifractality and efficiency of four series are investigated. Firstly, a new index evaluating the market efficiency degree based on intrinsic multifractality is developed. Secondly, the apparent multifractality and dynamic influences of the March 2020 crash on the market efficiency of the returns of insurance stock markets are investigated. The robustness of results is tested under the sample restriction. The empirical results reveal that four return series have multifractal characteristics. The stronger multifractal features and the greater multifractal degree are illustrated after the March 2020 crash. The traditional index overestimates the market inefficiency degrees of the four series. There are greater inefficiency degrees after the March 2020 crash. The effects of the March 2020 crash are stronger from the perspective of the new index and the efficiency of the returns of insurance stock markets are more affected by such crashes. Moreover, the inefficiency of developed insurance markets is more affected by such crashes.</p>