A bstract An analysis of the flavour oscillations of the charmed neutral meson is presented. The ratio of D 0 → K + π − and D 0 → K − π + decay rates is measured as a function of the decay time of the D 0 meson and compared with the charge-conjugated system to search for charge-parity violation. The meson flavour at production is double-tagged by the charges of the muon and pion in the preceding $$ \overline{B}\to {D}^{\ast }{(2010)}^{+}{\mu}^{-}X $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:msup> <mml:mfenced> <mml:mn>2010</mml:mn> </mml:mfenced> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>μ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mi>X</mml:mi> </mml:math> and D ∗ (2010) + → D 0 π + decays, respectively. These decays are selected from proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 5.4 fb − 1 . The flavour oscillation parameters, relating to the differences in mass and width of the mass eigenstates, are found to be y ′ = (5.8 ± 1.6) × 10 − 3 and ( x ′) 2 = (0.0 ± 1.2) × 10 − 4 . No evidence for charge-parity violation is seen either in the flavour oscillations or in the decay, where the direct charge-parity asymmetry is measured to be A D = (2.3 ± 1.7) %.