This paper is devoted to the Cramer Rao bound (CRB) on the angle and range of a narrow-band near-field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter. First, we prove that the conditional and unconditional CRBs are proportional for an arbitrary parametrization of the steering vector. Then, a Taylor expansion of the CRB is conducted to obtain accurate non-matrix closed-form expressions of the CRB on angle and range. In contrast to the existing expressions, our expressions are simple, interpretable and more general because the sensors are only constrained to be placed along some axis. Our analysis leads to the characterization of a class of centro-symmetric linear arrays with better near-field angle and range estimation capabilities