If $X\subset\mathbb{P}^n$ is a smooth subvariety and the normal bundle splits then, by adjunction, $X$ is subcanonical i.e. $\omega_{X}\cong\mathcal{O}_X(k)$. This is important for the following result in codimension two.

In *"Bénédicte Basili and Christian Peskine, Décomposition du fibré normal des surfaces lisses de $\mathbb{P}^4$ et structures doubles sur les solides de $\mathbb{P}^5$, Duke Math. J.
Volume 69, Number 1 (1993), 1-245"*, you can find the following result:

Let $X\subset\mathbb{P}^N$, $n\geq 4$ be a smooth codimension two subvariety. If $N_X$ splits then $X$ is a complete intersection.

For curves in $\mathbb{P}^3$ is quite different and the following is still an open problem: "Let $C\subset\mathbb{P}^3$ be a smooth, connected curve. Is it true that if $N_C = \mathcal{O}_C(a)\oplus\mathcal{O}_C(b)$, then $C$ is a complete intersection?"

On the normal bundle of submanifolds of $\mathbb{P}^n$by Lucian Badescu. Here is the link: arxiv.org/pdf/math/0701487.pdf – Mahdi Majidi-Zolbanin Feb 9 '13 at 20:25