This article investigates the relationship between daily crude oil prices and excange rates. Functional data analysis is used to show the clustering pattern of exchange rates and oil prices over the time period through high dimensional visualizations. We select exchange rates for important currencies related to crude oil prices by using the objective variable selection method. The selected sample data exhibits non-normal distribution with fat tails and skewness. Under the non-normality of the return series, we use copula funtions that do not require to assume the bivariate normality to consider marginal distribution. In particular, our study applies the popular and powerful statistical methods such as Gaussian copula partial correlations and Gaussian copula marginal regression. We find evidence of significant dependence for all considered pairs, except for the Mexican peso-Brent. Our empirical results show that the rise in the WTI oil price returns is associated with a depreciation of the US dollar.