  Time-dependent $CP$ asymmetries in the decay rates of the singly
Cabibbo-suppressed decays $D^0\rightarrow K^-K^+$ and $D^0\rightarrow
\pi^-\pi^+$ are measured in $pp$ collision data corresponding to an integrated
luminosity of 3.0 fb$^{-1}$ collected by the LHCb experiment. The $D^0$ mesons
are produced in semileptonic $b$-hadron decays, where the charge of the
accompanying muon is used to determine the initial state as $D^0$ or
$\bar{D}^0$. The asymmetries in effective lifetimes between $D^0$ and
$\bar{D}^0$ decays, which are sensitive to indirect $CP$ violation, are
determined to be \begin{align*}
  A_{\Gamma}(K^-K^+) = (-0.134 \pm 0.077 \; {}^{+0.026}_{-0.034})\% \,
  A_{\Gamma}(\pi^-\pi^+) = (-0.092\pm 0.145 \; {}^{+0.025}_{-0.033})\% \,
\end{align*} where the first uncertainties are statistical and the second
systematic. This result is in agreement with previous measurements and with the
hypothesis of no indirect $CP$ violation in $D^0$ decays.
