An assumption of uncorrelated observation errors is commonly adopted in conventional data assimilation. For this reason, high‐resolution data are resampled with strategies such as superobbing or data thinning. These strategies diminish the advantages of high temporal and spatial resolutions that can provide essential details in convection development. However, assimilating high‐resolution data, such as radar radial wind, without considering observation error correlations can lead to overfitting and thus degrade the performance of data assimilation and forecasts. This study uses a radar ensemble data assimilation system that combines the Weather Research and Forecasting model and Local Ensemble Transform Kalman Filter (WRF‐LETKF) to assimilate radar radial wind and reflectivity data. We present a strategy to include the error correlation of the Doppler radar radial wind in the WRF‐LETKF radar assimilation system and examine its impact on the accuracy of short‐term precipitation predictions based on a heavy rainfall event on June 2, 2017 in Taiwan. For radial wind, the horizontal error correlation scale is approximately 25 km according to the innovation statistics. The introduction of observation error correlation for radar radial wind assimilation produces more small‐scale features in wind analysis corrections compared to the experiment using an independent observation assumption. Consequently, the modification of wind corrections leads to stronger convergence accompanied by higher water vapor content, which enhances local convections. This results in more accurate simulations of reflectivity and short‐term precipitation. In particular, this advantage is identified for extreme heavy rainfall thresholds at small scales according to probability quantitative precipitation forecasts and fractions skill score.