For a quadrangle $P$, we consider the centroid $G_0$ of the vertices of $P$, the perimeter centroid $G_1$ of the edges of $P$ and the centroid $G_2$ of the interior of $P$, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle $P$ is a parallelogram. We denote by $M$ the intersection point of two diagonals of $P$. In this note, first of all, we show that if $M$ is equal to $G_0$ or $G_2$, then the quadrangle $P$ is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point $M$ of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point $M$ of diagonals.