The branching ratio for the decay of the tau lepton into at least one neutral kaon meson was measured from a sample of 201850 tau decays recorded by the OPAL detector from 1991 to 1995. The selection yielded 305 t-→X- K0 Lnt candidates (the charge conjugate is implied for all reactions), where X- is any charged hadron possibly accompanied by a neutral particle, giving a branching ratio of B&parl0;t-→X- K 0Lnt&parr0;=&parl0; 10.01±0.79±0.64&parr0;×10- 3, where the first error is statistical and the second is systematic. From the sample of t-→X- K0 Lnt decays, three exclusive decay modes were identified and their branching ratios were measured to be B&parl0;t-→p- K0nt&parr0; =9.1±0.9± 0.6×10-3, B&parl0;t-→p- K0≥1p0n t&parr0;=3.6± 1.3±1.0×10-3, B&parl0;t-→K- K 0≥0p0nt&parr0; =3.3±0.9±0.7 ×10-3, where the first error is statistical and the second is systematic. The t- →K*892 -nt branching ratio was determined to be 0.0140 ± 0.0013 using the t- →p-K 0nt branching ratio and assuming isospin conservation. Finally, the ratio of the non-strange decay constant fr to the strange decay constant fK* was measured to be 0.93 ± 0.05
