In recent decades, the recurrent occurrence of destructive floods in the Kan basin, located in western Tehran, has highlighted the need for a more detailed analysis of the rainfall–runoff relationship. This study aims to investigate the statistical dependence between annual peak instantaneous discharge and the maximum daily rainfall on flood days over 24, 48, and 72-hour durations using copula functions. After assessing the correlation between variables with Kendall’s tau and Spearman’s rho tests, the best-fitting marginal and copula distributions among the Frank, Gumbel, Clayton, and Plackett models were selected based on the Cramér–von Mises test and AIC and BIC criteria. The results indicate that the Soleghan and Kiga sub-basins exhibit stronger rainfall–discharge dependence, and that increasing the rainfall duration from 24 to 72 hours enhances the likelihood of simultaneous occurrence of rainfall and flood events (joint return period). Moreover, conditional return period analysis reveals that exceeding critical rainfall thresholds significantly increases peak discharge and prolongs the conditional return period. These findings suggest that long-duration rainfall plays a decisive role in generating major floods, and that instantaneous rainfall intensity alone is not a sufficient indicator for flood hazard assessment. The proposed framework can serve as a practical tool for risk estimation, the design of flood control structures, prioritization of watershed management interventions, and the development of early warning systems in similar catchments.