Climate policy is essential for fostering sustainable development and addressing climate-related issues, while climate policy uncertainty (CPU) introduces complex challenges in providing a consistent framework for action. In this study, we delve into the spillover dynamics among China's domestic CPU, foreign CPU, physical assets, and financial assets across various market scenarios, through a quantile-based connectedness method and evidence from China. The findings reveal: (1) The spillover dynamics are asymmetric across quantiles and time, and the COVID-19 pandemic influences the total connectedness. (2) The complexity of spillover patterns in physical assets is likely contingent upon market conditions, policy sources, asset types, and industrial-chain positions, while the spillovers of financial assets are quantile-dependent and time-varying, with the agricultural equity market showing relative resilience to the pandemic. (3) There is no significant Granger causality in quantiles between domestic CPU and foreign CPU under the entire sample period, and the rankings regarding the spillovers from CPUs to assets vary across market conditions. Implications for policymakers, investors, and firms are provided.