Chinese A- and H– share markets operate in different institutional environments (emerging/developing v.s. developed) and thus may have different tail risk properties. This paper focuses on the analysis of heavy-tailedness properties of these two markets using recently developed robust inference methods. The equality of tail indices of returns for A and H dual-listed companies cannot be rejected, and some A- and H– share returns may have infinite second moments. Their heavy-tailedness properties did not change significantly with respect to the 2008 financial crisis and the date when the corresponding company starts to be dual-listed.