Carbon fiber reinforced polymers (CFRPs) are valued in aerospace and other weight-conscious applications for their high strength-to-weight ratio. However, with the adoption of these lightweight materials emerges challenges not seen in traditional monolithic materials such as complex internal (i.e. outwardly invisible) damages like delamination or fiber failure in the structure. Robust methods of damage detection and health monitoring are therefore important. It is also desirable to utilize an intrinsic property of these materials, such as electrical conductivity, as an indicator of damage to render the material as self-sensing. Electrical impedance tomography (EIT) has been widely explored for damage detection and health monitoring in self-sensing materials. To date, however, studies involving EIT have been largely limited to materials with less electrical anisotropy than is seen in CFRPs and using only edge-placed electrodes (e.g. electrodes placed on the edges of a plate). These limitations are important because the inability to handle highly electrically anisotropic materials precludes EIT from a great number of existent CFRP structures. Furthermore, many real structures lack well-defined edges on which electrodes can be placed. In this paper, we tackle these challenges by presenting a preliminary study into the role of EIT sensitivity matrix formulation and surface-mounted electrodes on damage detection and localization in CFRPs. In our approach, the conductivity is modeled as being anisotropic, and the sensitivity matrix is formed using three methods — with respect to a scalar multiple of the conductivity tensor, the out-of-plane conductivity, and the in-plane conductivity. It was found that through-hole damage can be adeptly identified using the combination of surface-mounted electrodes and a sensitivity matrix formed with respect to either a scalar multiple of the conductivity tensor or the in-plane conductivity. The findings presented in this work take an important step towards translating EIT out of the laboratory and into real applications on CFRPs.