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We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi$ belonging to the ${(k,\mu )}^{\text{'}}$-nullity distribution and $(k,\mu )$-nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $\xi$ belonging to ${(k,\mu )}^{\text{'}}$- and $(k,\mu )$-nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $\xi$ belonging to ${(k,\mu )}^{\text{'}}$-nullity distribution...