The superconducting gap structure of a topological crystalline insulator (TCI) candidate ZrRuAs ($T^{rm on}_{rm c}$ = 7.9(1) K) with a noncentrosymmetric crystal structure has been investigated using muon spin rotation/relaxation ($mu$SR) measurements in transverse-field (TF) and zero-field (ZF) geometries. We also present the results of magnetization, electrical resistivity and heat capacity measurements on ZrRuAs, which reveal bulk superconductivity below 7.9~K. The temperature dependence of the effective penetration depth obtained from the analysis of the TF-$mu$SR spectra below $T_{rm c}$ is well described by an isotropic $s$-wave gap model as also inferred from an analysis of the heat capacity in the superconducting state. ZF $mu$SR data do not show any significant change in the muon spin relaxation rate above and below the superconducting transition temperature indicating that time-reversal symmetry is preserved in the superconducting state of this material.
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