We report on low energy muon measurements performed on 100 nm and 28 nm thin epitaxial, highly strained and twin free TbMnO₃ films grown on (110) YAlO₃ substrates by pulsed laser deposition (λ = 248 nm, ν = 2 Hz, T_S = 760°C). These investigations were done at the LEM beamline at the PSI, Switzerland which allowed for depthdependent analysis of the muon spin relaxation rate as a function of temperature. A clear decrease of the relaxation rates could be observed in regions near the substrate/thin film interface compared to measurements at the surface or in the middle of the films. This behavior could be attributed to a straininduced change of the Tb spin dynamics. Furthermore, it could be shown that the films are fully magnetic below a temperature of 40 – 50 K, which agrees well with susceptibility measurements performed on these films as well as with the bulk literature value of T_N,Mn = 41 K.