The interconnection between hard electronics and soft textiles remains a noteworthy challenge in regard to the mass production of textile-electronic integrated products such as sensorized garments. The current solutions for this challenge usually have problems with size, flexibility, cost, or complexity of assembly. In this paper, we present a solution with a stretchable and conductive carbon nanotube (CNT)-based paste for screen printing on a textile substrate to produce interconnectors between electronic instrumentation and a sensorized garment. The prototype connectors were evaluated via electrocardiogram (ECG) recordings using a sensorized textile with integrated textile electrodes. The ECG recordings obtained using the connectors were evaluated for signal quality and heart rate detection performance in comparison to ECG recordings obtained with standard pre-gelled Ag/AgCl electrodes and direct cable connection to the ECG amplifier. The results suggest that the ECG recordings obtained with the CNT paste connector are of equivalent quality to those recorded using a silver paste connector or a direct cable and are suitable for the purpose of heart rate detection.