  We propose and study a BCJ double-copy of massive particles, showing that it
is equivalent to a KLT formula with a kernel given by the inverse of a matrix
of massive bi-adjoint scalar amplitudes. For models with a uniform non-zero
mass spectrum we demonstrate that the resulting double-copy factors on physical
poles and that up to at least 5-particle scattering, color-kinematics
satisfying numerators always exist. For the scattering of 5 or more particles,
the procedure generically introduces spurious singularities that must be
cancelled by imposing additional constraints. When massive particles are
present, color-kinematics duality is not enough to guarantee a physical
double-copy. As an example, we apply the formalism to massive Yang-Mills and
show that up to 4-particle scattering the double-copy construction generates
physical amplitudes of a model of dRGT massive gravity coupled to a dilaton and
a two-form with dilaton parity violating couplings. We show that the spurious
singularities in the 5-particle double-copy do not cancel in this example, and
the construction fails to generate physically sensible amplitudes. We
conjecture sufficient constraints on the mass spectrum, which in addition to
massive BCJ relations, guarantee the absence of spurious singularities.
