An arborescence of a directed graph Γ is a spanning tree directed toward a particular vertex v . The arborescences of a graph rooted at a particular vertex may be encoded as a polynomial A v ( Γ ) representing the sum of the weights of all such arborescences. The arborescences of a graph and the arborescences of a covering graph Γ ˜ are closely related. Using voltage graphs to construct arbitrary regular covers, we derive a novel explicit formula for the ratio of A v ( Γ ) to the sum of arborescences in the lift A v ˜ ( Γ ˜ ) in terms of the determinant of Chaiken’s voltage Laplacian matrix, a generalization of the Laplacian matrix. Chaiken’s results on the relationship between the voltage Laplacian and vector fields on Γ are reviewed, and we provide a new proof of Chaiken’s results via a deletion-contraction argument.