Recent observations by the James Webb Space Telescope (JWST) have uncovered a substantial population of high-redshift Active Galactic Nuclei (AGN), reigniting the debate over their potential contributions to cosmic reionization. This study leverages archival X-ray data from the Chandra and XMM telescopes to examine 900 galaxies, identified as local analogs to those from the reionization era. These galaxies are notable for their compact structures, low mass, and intense emission features, comparable to early universe dwarf galaxies at redshift z>7. From a selection of 29 archival observations, nine displayed X-ray detections at S/N>3 with 2-10 keV X-ray luminosity > 10^(40) erg/s. These sources, along with six additional ones, also showed high ionization emission lines such as He IIλ4686. And in all these sources, a broad Hα line was detected. The weak correlation between the line widths of these emissions suggests that the X-ray emitting radiation is not a super-Eddington black hole X-ray binary, or neutron star X-ray binary. The X-ray emission observed is a few orders of magnitude higher than what one would expect from Wolf-Rayet stars and supernovae-driven winds. Hence, to produce the observed X-ray luminosity, low-luminosity AGN harboring intermediate mass black holes is necessary. The broad Hα-based BH measurements suggests BH masses to range between 10^4 and 10^6 Msun. The significant role of these local analogs, known as Lyman Continuum leakers, posits a compelling argument for the involvement of LLAGN in the mechanisms driving cosmic reionization.