  Inspired by the recent discovery of a doubly charmed tetraquark state
$T_{cc}^+$ by the LHCb Collaboration, we employ the effective Lagrangian
approach to investigate the decay width of $T_{cc}^{+}\to D^{+}
D^{0}\pi^{0}/D^{0} D^{0}\pi^{+}$ and $T_{cc}^{+}\to D^{0}D^{+}\gamma$ with the
assumption that $T_{cc}^{+}$ is an isoscalar $DD^{\ast}$ molecule. We show that
both the $T_{cc}\to D D\pi$ and $T_{cc}\to DD\gamma$ modes contribute to the
decay width of $T_{cc}$, with the former being dominant. The resulting total
decay width of about $\Gamma=63$ keV is smaller than the experimental decay
width obtained from the Breit-Wigner fit of the LHCb data, $\Gamma=410\pm
165\pm 43^{+18}_{-38}$ keV, while close to the number obtained from the
alternative unitary analysis, $\Gamma=48\pm 2^{+0}_{-14}$ keV, which supports
the molecular nature of $T_{cc}$.
