  The aim of this paper is characterize a class of contact metric manifolds
admitting $\ast$-conformal Ricci soliton. It is shown that if a $(2n +
1)$-dimensional $N(k)$-contact metric manifold $M$ admits $\ast$-conformal
Ricci soliton or $\ast$-conformal gradient Ricci soliton, then the manifold M
is $\ast$-Ricci at and locally isometric to the Riemannian of a flat $(n +
1)$-dimensional manifold and an $n$-dimensional manifold of constant curvature
4 for $n > 1$ and flat for $n = 1$. Further, for the first case, the soliton
vector field is conformal and for the $\ast$-gradient case, the potential
function $f$ is either harmonic or satisfy a Poisson equation. Finally, an
example is presented to support the results.
