The general theory of analytic energy gradients is presented for the state-specific multireference coupled cluster method introduced by Mukherjee and co-workers [Mol. Phys. 94, 157 (1998)], together with an implementation within the singles and doubles approximation, restricted to two closed-shell determinants and Hartree-Fock orbitals. Expressions for the energy gradient are derived based on a Lagrangian formalism and cast in a density-matrix notation suitable for implementation in standard quantum-chemical program packages. In the present implementation, we exploit a decomposition of the multireference coupled cluster gradient expressions, i.e., lambda equations and the corresponding density matrices, into a so-called single-reference part for each reference determinant and a coupling term. Our implementation exhibits the proper scaling, i.e., O(dN6) with d as the number of reference determinants and N as the number of orbitals, and it is thus suitable for large-scale applications. The applicability of our multireference coupled cluster gradients is illustrated by computations for the equilibrium geometry of the 2,6-isomers of pyridyne and the pyridynium cation. The results are compared to those from single-reference coupled cluster calculations and are discussed with respect to the future perspectives of multireference coupled cluster theory.