The Paris Agreement (COP21) sets out a global framework to limit global warming below 2C. Therefore, the target of carbon neutrality has a key role. In this context, countries have implemented cap-and-trade markets of carbon emissions allowances to manage the impact of CO2 released by companies. Over recent years, cryptocurrencies have given a new drive to pollution because of the massive energy consumption of mining activity. This paper investigates the tail relationship between the carbon credit market and the price of Bitcoin. For this purpose, we use two novel econometric models: the multivariate-quantile conditional autoregressive (MVMQ-CAViaR) model and Granger causality across quantiles. The results suggest that there is a downside risk spillover, i.e., tail co-dependence. We find that Bitcoin spillovers have a stronger impact on the carbon market. On the other hand, we show that the carbon market does not Granger-cause Bitcoin. The results of the Granger analysis confirm the multivariate quantile model's findings, i.e., Bitcoin influences the carbon market in the lower quantiles. We deem our results useful for policymakers to improve the framework of carbon emissions allowances.