The wireless capture of analog differential signals from fully passive (battery-less) sensors is technically challenging but it can allow for the seamless capture of differential biosignals such as an electrocardiogram (ECG). This paper presents a novel design for the wireless capture of analog differential signals using a novel conjugate coil pair for a wireless resistive analog passive (WRAP) ECG sensor. Furthermore, we integrate this sensor with a new type of dry electrode, namely conductive polymer polypyrrole (PPy)-coated patterned vertical carbon nanotube (pvCNT) electrodes. The proposed circuit uses dual-gate depletion-mode MOSFETs to convert the differential biopotential signals to correlated drain-source resistance changes and the conjugate coil wirelessly transmits the differences of the two input signals. The circuit rejects (17.24 dB) common mode signals and passing only differential signals. We have integrated this novel design with our previously reported PPy-coated pvCNT dry ECG electrodes, fabricated on a stainless steel substrate with a diameter of 10 mm, which provided a zero-power (battery-less) ECG capture system for long duration monitoring. The scanner transmits an RF carrier signal at 8.37 MHz. The proposed ECG WRAP sensor uses only two complementary biopotential amplifier circuits, each of which has a single-depletion MOSFET. The amplitude-modulated RF signal is envelope-detected, filtered, amplified, and transmitted to a computer for signal processing. ECG signals are collected using this WRAP sensor and compared with a commercial counterpart. Due to the battery-less nature of the ECG WRAP sensor, it has the potential to be a body-worn electronic circuit patch with dry pvCNT electrodes that stably operate for a long period of time.