Constitutive relations for rigid base-pair and continuum rod models of DNA are discussed.  First, a method to extract a complete set of sequence-dependent energy parameters for a rigid base-pair model from Molecular Dynamics (MD) simulations is described.  The method is properly consistent with equilibrium statistical mechanics, and leads to effective inertia parameters for the base-pair units as well as stacking and stiffness  parameters for the base-pair junctions.  Explicit formulas are  given that yield a complete set of base-pair model parameters in terms of equilibrium averages that can be estimated from a time series generated in an MD simulation.  The expressions to be averaged depend strongly both on the choice of coordinates used to describe rigid body orientations, and on the choice of strain measures at each junction.  Second, matching relations for passing parameters between the base-pair and continuum rod models are presented.  The relations provide an explicit correspondence between the parameters in a base-pair model with a non-standard choice of junction variables and those in a discretized rod model.