The paper deals with spectral properties of the Sturm-Liouville operator \(A\) associated to an indefinite differential expression of the form \[ \frac{1}{r} \biggl(-\frac{d}{dx} \biggl(p \frac{d}{dx} \biggl) + q\biggl), \] where \(p^{-1},q,r \in L_{\text{loc}}^{1} (\mathbb{R})\) are assumed to be real valued functions such that \(p > 0\) and \(r \neq 0\) for a.a. \(x \in \mathbb{R}\). The operator \(A\) is considered in the Krein space \(L_{r}^{2} (\mathbb{R})\). The author describes conditions under which the indefinite Sturm-Liouville operator \(A\) is locally definitizable.