We shall deduce some special regularity properties of solutions to the IVP associated to the Kadomtsev--Petviashvili equation. Mainly, for datum $u_0\in X_s(\mathbb{R}^2)$, $s>2$ (see (1.2) below) whose restriction belongs to $H^m((x_0,\infty)\times\mathbb{R})$ for some $m\in\mathbb{Z}^+,\,m\geq 3,$ and $x_0\in \mathbb{R}$, we shall prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^m((\beta,\infty)\times\mathbb{R})$ for any $\beta\in \mathbb{R}$ and any $t>0$.