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We investigate the dynamic correlation between the Bitcoin price (BTC) and the U.S. economic policy uncertainty index (USEPU) from the perspective of multifractality. Utilizing the multifractal detrended cross-correlation analysis (MF-DCCA), we confirm a long-range cross-correlation between BTC and USEPU. Moreover, the empirical results of MF-DCCA show that the power-law properties and multifractal characteristics between BTC and USEPU are significant. We further examine the long-range dependency of cross-correlation between BTC and USEPU series via the Hurst exponent test and confirm the durable cross-correlation. Finally, we introduce another multifractal indicator and examine the extent of multifractality among time series. The empirical results indicate that the BTC series, USEPU series, and the cross-correlation of BTC-USEPU present apparent multifractality, where BTC shows the strongest degree of multifractality.