We have investigated the N2O-HDO molecular complex using ab initio calculations at the CCSD(T)-F12a/aug-cc-pVTZ level of theory and using cavity ring-down spectroscopy to probe an HDO/N2O/Ar supersonic jet around 1.58 mu m. A single a-type vibrational band was observed, 13cm(-1) redshifted compared to the OH+OD excited band in HDO, and 173 vibration-rotation lines were assigned (T-rot approximate to 20K). A weighted fit of existing microwave and present near infrared (NIR) data was achieved using a standard Watson's Hamiltonian (sigma = 1.26), producing ground and excited states rotational constants. The comparison of the former with those calculated ab initio suggests a planar geometry in which the OD rather than the OH bond in water is almost parallel to NNO. The equilibrium geometry and dissociation energy (D-e = -11.7 kJ/mol) of the water-nitrous oxide complex were calculated. The calculations further demonstrate and allow characterising another minimum, 404cm(-1) (Delta E-0) higher in energy. Harmonic vibrational frequencies and dissociation energies, D-0, were calculated for various conformers and isotopic forms of the complex, in both minima. The absence of N2O-D2O from dedicated NIR experiments is reported and discussed.