if $h^T D \psi = 0 \forall h \in \mathbb{R}^N$, then what can we say about $\psi$ and $D$?

Question

$D$ is a $N \times M$ matrix. $h \in \mathbb{R}^N$ and $\psi \in \mathbb{R}^M$

Would this mean that $\psi$ is in the Nullspace of $D^T$. because irrespective of h, $D$ is transforming these to $0$; which would happen only if $\psi$ is in the nullspace or $D = 0$?

What can we now say about the rows of D?