This paper studies the dependence between crude oil and RCEP stock markets before and after COVID-19 by using local Gaussian correlations, contagion tests, and time-frequency domain causality tests. Empirical results show that the lower tail dependence considerably enhanced except in China, while the higher tail dependence significantly increased in Australia, New Zealand, Japan, and Thailand. Contagion is detected from the WTI oil to New Zealand and Thailand stocks. The crude oil market has a short-term (0–32 day frequency) effect on RCEP stock markets, whereas the RCEP stock markets have a relatively stronger, long-term (64–128 day frequency) impact on crude oil markets. RCEP public panic disrupted the oil and stock markets during the Delta and Omicron spread. These findings may help the RCEP governments, institutions, and investors boost energy cooperation, capital flow, and cross-border investments under different market states and investment horizons.