  We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times
k,$ namely the slab of width $k$. Each edge is assigned independently a passage
time of either 0 (with probability $1-p_c(\mathbb{S}_k)$) or 1 ((with
probability $p_c(\mathbb{S}_k)$) where $p_c$ is the critical probability. We
prove central limit theorems for point-to-point and point-to-line passage
times. These generalize the results of [Kesten and Zhang] to non-planar graphs.
