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We investigate the gap symmetry of the topological superconductor candidate HfRuP, which crystallizes in a noncentrosymmetric hexagonal crystal structure, using muon spin rotation/relaxation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>SR) measurements in transverse-field (TF) geometry. The temperature and magnetic field dependencies of the superconducting relaxation rate derived from the TF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>SR spectra can be well described by an isotropic <i>s</i>-wave gap. The superconducting carrier density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>n</mi><mi>s</mi></msub></semantics></math></inline-formula> = 1.41(1) × 10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>26</mn></msup></semantics></math></inline-formula> m<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula> and the magnetic penetration depth, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>(0) = 603(2) nm, were calculated from the TF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>SR data. Interestingly, the ratio between the superconducting transition temperature and the superfluid density, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>/<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></semantics></math></inline-formula>(0) ∼ 3.3, is very close to those of unconventional superconductors. Further, our zero-field (ZF) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>SR results do not show any considerable change in the muon spin relaxation above and below the superconducting transition temperature, suggesting that time-reversal symmetry is preserved in the superconducting state of this superconductor.