The paper examined Ti3C2Tx MXene (T—OH, Cl or F), which is prepared by etching a layered ternary carbide Ti3AlC2 (312 MAX-phase) precursor and deposited on a polycaprolactone (PCL) electrospun membrane (MXene-PCL nanocomposite). X-ray Diffraction analysis (XRD) and Scanning Electron Microscopy (SEM) indicates that the obtained material is pure Ti3C2 MXene. SEM of the PCL-MXene composite demonstrate random Ti3C2 distribution over the nanoporous membrane. Results of capacitance, inductance, and phase shift angle studies of the MXene-PCL nanocomposite are presented. It was found that the frequency dependence of the capacitance exhibited a clear sharp minima in the frequency range of 50 Hz to over 104 Hz. The frequency dependence of the inductance shows sharp maxima, the position of which exactly coincides with the position of the minima for the capacitance, which indicates the occurrence of parallel resonances. Current conduction occurs by electron tunneling between nanoparticles. In the frequency range from about 104 Hz to about 105 Hz, there is a broad minimum on the inductance relationship. The position of this minimum coincides exactly with the position of the maximum of the phase shift angle—its amplitude is close to 90°. The real value of the inductance of the nanocomposite layer was determined to be about 1 H. It was found that the average value of the distance over which the electron tunnels was determined with some approximation to be about 5.7 nm and the expected value of the relaxation time to be τM ≈ 3 × 10−5 s.