  In this paper, we present a classification of $ N(\kappa)$-contact metric
manifolds with using some special flatness conditions on $ \mathcal{T}
$-curvature tensor. We examine $\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, $
\xi$-$\mathcal{T}$-flat and $ \varphi $-$\mathcal{T}$-flat $ N(\kappa)$-contact
metric manifolds .Also,we consider the conditions $ \mathcal{T}(\xi,X).R=0 $
and $ \mathcal{T}(\xi,X).S=0 $ for the Riemannian curvature tensor $ R $ and
Ricci curvature tensor $ S $. Thus, we obtain a classification of $
N(\kappa)$-contact metric manifolds.
