It has been known that testing of reversible circuits is relatively easier than conventional irreversible circuits in the sense that few test vectors are needed to cover all stuck-at faults. This paper shows, however, that it is NP-hard to generate a minimum complete test set for stuck-at faults on the wires of a reversible circuit using a polynomial time reduction from 3SAT to the problem. We also show non-trivial lower bounds for the size of a minimum complete test set.