Meteorites represent the recoverable portions of asteroids occurring between Mars and Jupiter within the solar system that reach the surface of the Earth. Meteorites are rare extraterrestrial objects studied extensively to improve understanding of planetary evolution. In this work, calibration-free laser-induced breakdown spectroscopy (CF-LIBS) evaluates quantitative elemental and molecular analysis of the Dergaon meteorite, an H 4-5 chondrite fall sample, Assam, India. Spectral signatures of H, N, O, Na, Mg, Al, Si, P, K, Ca, Ti, Cr, Mn, Fe, Co, Ni, Ir, are measured. Along with the atomic emission, this work reports as well molecular emission from FeO molecules. The concentration of the measured elements obtained using CF-LIBS are in close agreement with earlier reports. The elements H, N and O and their concentrations are estimated using CF-LIBS for the first time. This study applies laser spectroscopy to establish presence of Ni, Cr, Co, and Ir in meteorites. Elemental analysis forms the basis for establishment of potential molecular composition of the Dergaon meteorite. Moreover, the elemental analysis approach bodes well for in-situ analyses of extraterrestrial objects including applications in planetary rover missions.