Structural Health Monitoring (SHM) uses sensors in advanced engineering structures to evaluate integrity and detect damage or deformation affecting structural performance, e.g. cracks, holes, or corrosion. Carbon fiber (CF) textile composites are commonly used to reinforce structures such as aircraft, vehicles, or bridges due to their high tensile strength to weight ratio, chemical resistance, and thermal and electrical conductivity. Printing electronics on textiles is a scalable manufacturing technology combining the physical properties of textile materials with the added functionality of electronic elements making them self-sensing. Extrusion printing is a contactless digital printing method to print electrical conductors and passive circuit elements. This paper proposes to combine conventional CF composite manufacturing processes with printed conductors to create self-sensing CF textile composites. Damage is sensed by measuring resistance changes in a CF sheet. Contacts are extrusion printed directly on woven CF sheets using silver flake ink. A multiplexed Kelvin Double Bridge circuit is the read-out interface. This allows small resistance changes due to damage to be measured in a four-point configuration. The circuit is connected to the printed contacts on the CF sheet through multiplexers to detect damage in different locations. This 2D digital sensor can detect the location and size of damage holes for SHM. The resolution of the sensor is controlled by the location and spacing of the silver electrodes, which were studied experimentally and by simulation. The resolution is 26 mm in the current direction and 16 mm in the orthogonal direction. The threshold of detectable damage is 4 mm2. Simulation of the sensor as an isotropic 2D conductor shows good agreement with experimental results for the orthotropic fabric. The resultant sensing device could be integrated into many composite structures as one of its layers or simply printed on the surface to create smart structures.