Based on annual maximum 1-day and 3-day rainfall data from the Changzhou precipitation station from 1951 to 2015, a joint distribution function was constructed using the Copula function, and the corresponding co-occurrence return period and risk of rainstorm combination were calculated. Then, the function was used to evaluate the probable return period and risk of a rainstorm in Changzhou City on June 26, 2015. The results show that the co-occurrence return period when the annual maximum 1-day and 3-day rainfall according to a certain design standard encounter is larger than the respective return periods of annual maximum 1-day and 3-day rainfall. The risk when two rainstorms with the same design frequency encounter is higher, and will decrease with the increase of the corresponding return period. The co-occurrence return period of the rainstorm in Changzhou on June 26 is 218 years, when the co-occurrence risk is only 17.4%, indicating that this rainstorm is special and rare. Flood control in Changzhou City still faces severe issues in the future.