Laser ablation molecular isotopic spectrometry (LAMIS) recently was reported for rapid isotopic analysis by measuring molecular emission from laser-induced plasmas at atmospheric pressure. This research utilized the LAMIS approach to study C₂ molecular formation from laser ablation of carbon isotopic samples in a neon gas environment at 0.1 MPa. The isotopic shift for the Swan system of the C₂ Δν = 1 band was chosen for carbon isotope analysis. Temporal and spatial resolved measurements of ¹²C₂, ¹²C¹³C, and ¹³C₂ show that C₂ forms from recombination reactions in the plasma. A theoretical simulation was used to determine the temperature from the molecular bands and to extract the isotopic ratio of ¹²C/¹³C derived from ¹²C₂, ¹²C¹³C, and ¹³C₂. Our data show that the ratio of ¹²C/¹³C varies with time after the laser pulse and with distance above the sample. ¹²C/¹³C deviates from the nominal ratio (2:1) at early times and closest to the sample surface. These measurements provide understanding of the chemical processes in the laser plasma and analytical improvement using LAMIS.