Division polynomials associated with an elliptic curve $E/K$ are polynomials $\phi _n, \psi _n^2$ that arise from the sequence of points $\{nP\}_{n \in \mathbb {N}}$ on this curve. If one wishes to study $\mathbb {Z}$-linear combination of points on $E(K)$, we can use net polynomials $\Phi _{\boldsymbol {v}}, \Psi _{\boldsymbol {v}}^2$ which are higher-dimensional analogs of division polynomials. It turns out that they are also elliptic nets, an $n$-dimensional array with values in $K$ satisfying the same nonlinear recurrence relation that division polynomials do as well. Now assume further that the elliptic curve $E/K$ has complex multiplication by an order of a quadratic imaginary field $F \subseteq K$, we will prove a formula for the common valuation of $\Phi _{\boldsymbol {v}}$ and $\Psi _{\boldsymbol {v}}^2$ associated with multiples of points by elements of an order in $F$. As an application, we will use the formula to show that elliptic divisibility sequences associated with multiples of points indexed by elements of an order also satisfy a recurrence relation when indexed by elements of an order, subject to certain conditions on the indices.