We report the realisation of a laser spectrometer in the mid-infrared spectral region based on difference-frequency generation in a periodically poled LiNbO3 crystal. Tunable coherent radiation around 3 microm was produced by mixing a diode-pumped monolithic cw Nd-YAG laser and an injection-locked diode laser at 0.785 microm. High sensitivity N2O detection was demonstrated by observing pure absorption spectra of lines in the v1 + v3 combination band. We estimate a minimum detectable pressure of pure N2O of 1 x 10(-2) Pa with 0.9 m absorption path-length, corresponding to an absorbance of 3 x 10(-4). Nitrous oxide was also detected in presence of O2, N2 and air. Collisional broadening coefficients for the P(33) line at 3447.678 per cm are reported for N2O-N2 and N2O-O2 mixtures.