From a sample of about 75000 τ decays identified with the ALEPH detector, K0 production in 1-prong hadronic decays is investigated by tagging the KL0 component in a hadronic calorimeter. Results are given for the final states ντh−K0 and ντh−π0K0 where the h− is separated into π and K contributions by means of the dE/dx measurement in in the central detector. The resulting branching ratios are: (Bτ → ντπ−K0) = (0.88±0.14±0.09)%, (Bτ → ντK−K0) = (0.29±0.12±0.03)%, (Bτ → ντπ−π0K0) = (0.33±0.14±0.07)% aand (Bτ → ντK−π0K0) = (0.05±0.05±0.01)%. The K∗ decay rate in the K0π channel agrees with that in the Kπ0 mode: the combined value for the branching ratio is .