Let $G=(V,E)$ be an undirected simple graph. The contraction of an edge $\{u,v\}\in E$ removes the vertices $u$ and $v$ from $G$ and replaces them with a new vertex that is made adjacent to precisely those vertices which were adjacent to $u$ or $v$ (without introducing self-loops or multiple edges). \par For a parameter $\pi$, let $ct_\pi(G)$ be the minimum number of edge contractions required to modify $G$ into a graph $H$ such that $\pi(H)=\pi(G)-1$. \par A set $D\subseteq V$ is a total dominating set of $G$ if and only if every vertex in $V$ has a neighbour in $D$, and the total domination number $\gamma_t(G)$ of $G$ is the size of a minimum total dominating set of $G$. A set $D\subseteq V$ is a semitotal dominating set of $G$ if and only if every vertex in $V-D$ has a neighbour in $D$ and every vertex in $D$ is at distance at most two from another vertex in $D$. The semitotal domination number $\gamma_{t2}(G)$ of $G$ is the size of a minimum semitotal dominating set of $G$. \par For $\pi\in\{\gamma_t,\gamma_{t2}\}$, the {\sc Contraction Number}$(\pi, k)$ problem is defined as follows: \par Instance: A graph $G$. \par Question: Is $ct_\pi(G)=k$? \par It is known that for $\pi\in\{\gamma_t,\gamma_{t2}\}$ and $k > 3$, every instance of {\sc Contraction Number}$(\pi, k)$ is always negative. Also, it is proved that {\sc Contraction Number}$(\pi, 1)$ is $\ssf{NP}$-hard. \par In this paper, it is shown that for $\pi\in\{\gamma_t,\gamma_{t2}\}$ and $k\in\{2,3\}$, {\sc Contraction Number}$(\pi, k)$ is $\ssf{NP}$-hard. Therefore, combined with previous results, the following dichotomy holds. \par Theorem 1. For $\pi\in\{\gamma_t,\gamma_{t2}\}$, {\sc Contraction Number}$(\pi, k)$ is $\ssf{NP}$-hard if and only if ${k \leq 3}$.